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ELEMENTS 


OF 


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DESIGNED  AS  A  TEXT-BOOK  FOR  ACADEMIES, 
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BY  AIONZO  GRAY,  A.M., 

PBOPESSOB  OF  CHEMISTRY  AND  NATURAL  PHILOSOPHY  IN  THE  BROOKLYN  FEMALB 
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UHI7ERSITY 


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89  CLIFF   STREET. 

1851. 


L   \\ 


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. 


PREFACE. 


THE  work  now  offered  to  the  public  was  originally  com- 
piled and  designed  for  the  use  of  pupils  under  the  imme- 
diate instruction  of  the  author. 

In  preparing  the  work,  the  object  has  been,  in  the 

First  place,  to  include  a  larger  amount  of  modern  sci- 
ence than  is  found  in  the  text-books  which  are  generally 
accessible  to  those  who  are  commencing  the  study  of  Nat- 
ural Philosophy,  and  at  the  same  time  to  give  as  much  of 
conciseness  and  clearness  to  the  different  branches  of  the 
science  as  was  consistent  with  their  nature  and  import- 
ance ;  and,  in  the 

Second  place,  to  prepare  a  text-book  which  should  be 
a  medium  between  the  larger  works  and  those  generally 
used  in  our  academies  and  higher  institutions. 

The  following  are  the  principal  features  of  the  work : 

At  the  head  of  each  section  an  analysis  is  given  in  the 
form  of  propositions,  in  order  that  the  student  may  have 
a  general  view  of  what  the  section  contains.  The  advant- 
age of  this  the  author  has  found,  by  long  experience,  to  be 
very  great,  as  it  fixes  in  the  memory  the  leading  and 
fundamental  principles  of  the  science,  and  habituates  the 
mind  to  analyze  and  systematize  the  various  topics  which 
may  come  under  review. 

Another  feature  of  the  work  is  the  introduction  of  ex- 
amples in  the  form  of  problems,  in  order  to  render  each 
principle  familiar,  and  to  enable  the  student  to  make  a 
practical  application  of  his  knowledge. 

For  the  purpose  of  directing  attention  to  the  more  im- 
portant parts  to  be  studied,  questions  are  added  at  the 


IV  PREFACE. 

foot  of  each  page.  These,  if  properly  used,  may  afford 
essential  aid  to  both  teacher  and  pupil.  It  is  expected, 
however,  that  the  teacher  will  add  many,  in  the  course  of 
recitation,  which  are  not  found  in  the  book,  for  it  is  be- 
lieved to  be  undesirable  to  have  a  large  number  of  ques- 
tions on  each  topic  prepared  beforehand  for  the  pupil. 

The  introduction  of  algebraic  formulae  and  geometrical 
demonstrations  has  been  mostly  confined  to  notes,  or  else 
such  portions  are  printed  in  smaller  type,  so  that  they 
may  be  omitted  by  those  who  are  not  familiar  with  alge- 
bra and  geometry.  Each  branch  of  the  subject,  as  will 
be  noticed,  is  very  fully  illustrated  by  diagrams  and  rep- 
resentations of  the  apparatus  which  is  usually  employed 
for  experimental  illustrations.  Many  experiments  are 
also  described,  so  that  a  teacher  is  at  once  provided  with 
the  means  of  teaching  by  experiment  and  of  confirming 
the  truth  of  the  most  important  propositions. 

In  the  compilation  of  the  work,  the  standard  writers  on- 
Natural  Philosophy  have  been  carefully  consulted,  but  it 
has  not  been  thought  expedient  to  give  all  the  references  ; 
in  fact,  it  would  be  difficult,  in  many  cases,  to  refer  to  the 
original  authors. 

In  order  to  obviate  the  inconvenience  arising  from 
changes  which  are  usually  made  in  text-books  after  the 
first  edition,  and  to  render  the  work  as  free  from  errors 
as  possible,  the  printed  sheets  were  first  used  in  the  in- 
struction of  a  class  ;  at  the  same  time,  they  were  subjected 
to  the  inspection  of  several  eminent  teachers  and  other 
scientific  friends,  whose  suggestions  have  been  of  great 
value  in  the  revision  and  reprinting-  of  the  work. 

The  author  would  acknowledge  his  obligations  to  Prof. 
E.  S.  Snell,  of  Amherst  College,  and  particularly  to  Prof. 
E.  Loomis,  of  the  New  York  University,  for  the  most  im- 
portant aid  in  this  particular.  A.  G. 

Brooklyn  Female  Academy,  Jan.,  1850. 


CONTENTS. 


INTRODUCTION Page  13 

CHAPTER  I. 

MATTER  AND  ITS  GOVERNING   FORCES. 
SECTION  I. 

OF    MATTER 19 

I.  Divisibility  of 19 

II.  Impenetrability  of 21 

III.  Indestructibility  of 22 

SECTION  II. 

OF    THE    FORCES    WHICH    GOVERN    MATTER    AND    PROPERTIES    RESULTING 

THEREFROM 24 

I.  Cohesive  Attraction 25 

II.  Capillary  Attraction 32 

III.  Chemical  Affinity 34 

IV.  Electrical  and  Magnetic  Attraction 35 

V.  Attraction  of  Gravitation 35 

VI.  Inertia 40 

CHAPTER  II. 

MOTION  AND  ITS  LAWS INERTIA. 

SECTION  I. 

OF  MOTION 41 

I.  Absolute 41 

II.  Relative 41 

III.  Apparent 42 

IV.  Real  .                                                               42 


VI  CONTENTS. 

SECTION  II. 

LAWS    OF    MOTION    IN    RELATION    TO    FORCES,   ESPECIALLY   TO   THE   FORCE 

OF  INERTIA Page  43 

First  Law  of  Motion 44 

Second  Law  of  Motion 49 

Third  Law  of  Motion 51 

SECTION  III. 

COMPOSITION   AND    RESOLUTION    OF    MOTION    AND    FORCES 56 

I.  Composition  of  Forces 56 

II.  Resolution  of  Forces 59 

SECTION  IV. 

GRAVITATION,    VARIABLE    FORCES,    AND    MOTIONS 60 

I.  Laws  of  falling  Bodies 61 

II.  Center  of  Gravity 67 

III.  Central  Forces 72 

TV.  Collision  of  Bodies 76 

CHAPTER  III. 

OP  THE  MECHANICAL    POWERS. 
SECTION  I. 

OF    THE    LEVER,    THE    WHEEL    AND    AXLE,    AND    THE    PULLEY...     81 

I.  The  Lever 82 

II.  Wheel  and  Axle 88 

HI.  The  Pulley 93 

SECTION  II. 

THE  INCLINED  PLANE,  THE  SCREW,  AND  THE  WEDGE 95 

I.  The  Inclined  Plane 96 

II.  The  Screw 106 

III.  The  Wedge 109 

SECTION  III. 

REGULATION    OF    MACHINERY  AND  MODIFICATIONS    OF    MOTION FRIC- 
TION   ". 109 

I.  Regulation  of  Motion 110 

II.  Modification  of  Mot' on ; Ill 

III.  Friction 113 

IV.  Strength  of  Materials 114 

V.  Utility  of  the  Mechanical  Powers 114 


CONTENTS.  Vll 

CHAPTER  IV. 
HYDRODYNAMICS. 

SECTION  I. 

HYDROSTATICS Page  119 

I.  Pressure  of  Liquids 131 

II.  Amount  of  Pressure 122 

III.  Result  of  the  Laws  of  Pressure 127 

IV.  Specific  Gravity 129 

V.  Floating  Bodies 133 

SECTION  II. 

HYDRAULICS 137 

I.  Laws  of  the  Efflux  of  Liquids 138 

II.  Influence  of  the  Orifice  upon  the  Quantity  discharged 142 

III.  Influence  of  conducting  Pipes  upon  the  Quantity  discharged  . .  143 

IV.  Form  of  the  Jet  of  a  spouting  Liquid 145 

V.  Motion  of  Liquids  in  Pipes,  &c 146 

VI.  Resistance  of  Liquids  to  Bodies  floating  in  them 148 

VII.  Water-wheels 151 

CHAPTER  V. 

PNEUMATICS. 
SECTION  I. 

PROPERTIES    OF    ATMOSPHERIC    AIR 156 

I.  The  Materiality  of  the  Air 157 

II.  Elasticity  of  the  Air 160 

III.  Pressure  of  the  Air 163 

IV.  Mechanical  Pressure  of  the  Air  on  Liquids  and  Solids 169 

V.  Force  of  compressed  Air 172 

VI.  Diffusion  of  Air  through  other  Matter 176 

VII.  Buoyancy  of  the  Air 178 

VIII.  Resistance  of  the  Air 178 

IX.  Motion  of  Air  and  other  Gases 180 

SECTION  II. 

THE  ATMOSPHERE METEOROLOGY 182 

I.  "Weight  of  the  Atmosphere 183 

II.  Density  of  the  Atmosphere 184 

III.  Height  >f  the  Atmosphere 186 


Vlll  CONTENTS. 

IV.  Temperature  of  the  Atmosphere Page  187 

V.  Phenomena  of  Winds 188 

VI.  Moisture  of  the  Atmosphere 193 

VII.  Meteorolites 198 

VIII.  Relations  of  the  Atmosphere  to  Animals  and  Vegetables 199 

IX.  Ventilation 199 

CHAPTER  V. 

OF    UNDULATIONS. 

I.  Origin  of  Undulations 207 

II.  Laws  of  Undulations 208 

HI.  Undulations  of  Liquids — Water-waves 213 

IV.  Undulations  of  Gases — Air-waves 219 

CHAPTER  VI. 

ACOUSTICS. 

SECTION  I. 

OF  SOUND 225 

I.  Sound-waves 226 

II.  Varieties  of  Sound 227 

III.  Varieties  of  Tone 228 

IV.  Conduction  of  Sound 228 

V.  Velocity  of  Sound 230 

VI.  Distance  to  which  Sound  may  be  propagated 232 

VII.  Reflection  of  Sound 233 

SECTION  II. 

MUSICAL    TONES 236 

I.  Relation  between  a  vibrating  String  and  musical  Notes 237 

II.  Musical  Tones  in  Pipes 240 

III.  Transmission  of  Tones 244 

IV.  Organs  of  Voice 245 

V.  Organs  of  Hearing 246 

CHAPTER  VII. 

OF    CALORIC    OR   HEAT. 

I.  Property  of  sensible  Calorie 248 

II.  Effect  of  sensible  Caloric 248 

III.  Insensible  Caloric  . .  .249 


CONTENTS.  lx 

IV.  Steam Page  249 

V.  Steam-engine ,  252 

CHAPTER  VIII. 

ELECTRICITY. 

SECTION  I. 

STATICAL,    OR    COMMON    ELECTRICITY 259 

I.  Modes  of  producing  Electricity 260 

II.  Modes  of  detecting  Electricity 262 

III.  Electrical  States  produced  by  Friction  of  different  Substances.  263 

IV.  Property  of  the  Electric  Fluid 266 

V.  Distribution  of  Electricity  on  Conductors 271 

VI.  The  Leyden  Jar 272 

VII.  Effects  of  Electricity 277 

VIII.  Electricity  of  the  Atmosphere 286 

IX.  Velocity  of  Electricity 290 

X.  Nature  of  Electricity 291 

SECTION  II. 

VOLTAIC    ELECTRICITY,    OR    GALVANISM 293 

I.  Electricity  produced  by  Contact 293 

II.  Electricity  generated  by  Chemical  Action 295 

III.  Quantity  of  Electricity  in  simple  and  compound  Circles 299 

IV.  Effects  of  Voltaic  Electricity 299 

SECTION  III. 

MAGNETIC    EFFECTS   OF   ELECTRICITY,    MAGNETISM,    ELECTRO-MAGNET- 
ISM, AND   MAGNETO-ELECTRICITY 303 

I.  Magnetism 304 

II.  Electro-magnetism 307 

III.  Influence  of  Voltaic  Currents  on  soft  Iron  and  Steel 310 

IV.  Volta-electric  Induction 313 

V.  Magneto-electric  Induction 316 

VI.  Theories  of  Magnetism,   Electro-magnetism,   and   Magneto- 
electricity 317 

VII.  Application  of  Electro-magnetism  to  useful  Purposes  320 

1.  Magnetic  Telegraphs 320 

2.  Electro-chronograph 322 

VIII.  Vital  Effects  of  Electricity 323 

IX.   Animal  Electricity 323 


X  CONTENTS. 

CHAPTER  IX. 

LIGHT,    OR    OPTICS. 
SECTION  I. 

ORIGIN    OF    LIGHT,   AND    THE    LAWS    WHICH    GOVERN    ITS    TRANSMIS- 
SION   Page  325 

I.  Origin  of  Light 326 

II.  Luminous  and  non-luminous  Bodies 327 

III.  Laws  of  the  Transmission  of  Light 328 

IV.  Intensity  of  Light 330 

V.  Velocity  of  Light 333 

SECTION  II. 

REFLECTION    OF    LIGHT,    OR    CATOPTRICS 334 

I.  Laws  of  the  Reflection  of  Light  from  Plane  Surfaces 335 

Images  formed  by  Plane  Mirrors 336 

II.  Laws  of  the  Reflection  of  Light  from  Curved  Surfaces 339 

Images  formed  by  Concave  Mirrors 341 

Images  formed  by  Convex  Mirrors 343 

SECTION  in. 

DIOPTRICS,    OR    REFRACTION    OF    LIGHT 344 

I.  Laws  of  Refraction 345 

II.  Refraction  of  Light  by  Prisms 349 

III.  Refraction  of  Light  by  Lenses 350 

IV.  Decomposition  of  Light 357 

V.  Application  of  the  Laws  of  Refraction  and  Reflection  to  the 

Explanation  of  Natural  Phenomena ^. 365 

SECTION  IV. 

OF    THE    EYE    AND    OPTICAL    INSTRUMENTS 371 

I.  Compound  Eyes 372 

II.  Simple  Eyes  with  Convex  Lenses 372 

III.  Distance  of  Distinct  Vision 373 

IV.  Optical  Instruments 376 

SECTION  V. 

THEORIES  OF  THE   NATURE   OF  LIGHT,  WITH  THEIR    ILLUSTRATION  AND 

APPLICATION 384 

I.  Theory  of  Emission 384 

II.  Theory  of  Undulations 384 


CONTENTS.  Xi 

III.  Interference  of  Light Page  386 

IV.  Polarization  of  Light 392 

1.  By  Reflection 392 

2.  By  Refraction 394 

V.  Double  Refraction 395 

SECTION  VI. 

CHEMICAL  AGENCY  OF  LIGHT,  AND  THE  CONNECTION  OF  LIGHT,  HlAT, 

AND  ELECTRICITY 39f* 

I.  Chemical  Agency  of  Light 40( 

II.  Photography 40( 

III.  Connection  of  Light,  Heat,  and  Electricity 401 


NOTE   TO  TEACHERS. 

THE  author  would  recommend  to  those  teachers  who  may  use  this  work 
to  adopt  a  method  which  he  has  employed  and  found  successful,  in  refer- 
ence to  the  analysis  at  the  head  of  each  section.  H©  has  been  accustom- 
ed to  require  his  pupils,  especially  in  the  junior  classes,  to  «o*nrart  thorough- 
ly to  memory  the  analysis  before  studying  the  section. 


UNI7EESITY 


[  N r  R  0  D  U  C  1  ION. 


THE  term  Philosophy  means  the  love  of  wisdom.  Its  object 
is  to  ascertain  the  causes  of  events,  or  of  changes  in  matter  and 
in  mind.  When  the  facts  or  phenomena  which  result  from  some 
common  cause  are  arranged  and  classified  in  accordance  with  cer- 
tain fixed  principles,  they  constitute  a  Science.  Mental  science 
consists  of  an  orderly  arrangement  of  the  laws  and  phenomena  of 
mind  ;  physical  or  material  science,  of  a  similar  arrangement  of 
facts  and  principles  which  relate  to  matter. 

Natural  Philosophy  is  that  science  which  relates  to  the  forces 
and  laws  which  govern  matter  in  masses.  Its  object,  therefore, 
is  to  attain  a  knowledge  of  forces  and  motions. 

The  science  of  Chemistry,  on  the  other  hand,  has  reference  to 
the  composition  of  bodies.  Its  object  is  to  ascertain  what  kinds 
of  matter  exist,  to  determine  the  forces  which  produce  the  compo- 
sition and  decomposition  of  masses,  and  the  laws  by  which  such 
forces  are  regulated. 

If  there  were  but  one  kind  of  matter,  as  water  or  iron,  there 
would  still  be  a  wide  field  open  for  the  natural  philosopher,  for 
he  does  not  regard  the  nature  of  matter,  but  simply  its  mechan- 
ical properties,  the  phenomena  of  perceptible  distance.  If  there 
were  not  more  than  one  kind  of  matter,  the  chemist  would  have 
no  subjects  for  investigation,  as  his  object  is  to  study  those  changes 
of  imperceptible  distance,  which  can  occur  only  when  two  or  more 
kinds  of  matter  are  in  apparent  contact. 

In  Natural  Philosophy  we  are  to  regard  masses  of  matter  as  a 
collection  of  very  small  particles  called  atoms,  all  similar  in  con- 
stitution, and  held  together,  in  solids  and  liquids,  by  a  force  of 

Meaning  of  Philosophy,  of  Science,  of  Natural  Philosophy,  of  Chemistry. 
Of  what  does  a  mass  of  matter  consist  ? 


14  INTRODUCTION. 

attraction  called  Cohesion,  and  in  gases  by  the  force  called  At- 
traction of  Gravitation. 

In  Chemistry,  too,  we  view  masses  of  matter  as  composed  of 
atoms,  but  they  are,  for  the  most  part,  different  from  the  preceding, 
in  the  fact  that  we  view  them  as  consisting  of  different  kinds  of 
matter,  and  capable  of  being  combined  together  by  a  force  called 
Chemical  Affinity,  and  by  such  a  combination  of  producing  com- 
pounds entirely  different  in  property  from  either  of  the  elements 
which  enter  into  the  combination.  Thus,  when  oxygen  and  hy- 
drogen gases  unite,  they  form  ^vater,  a  liquid,  different  in  every 
respect  from  either  oxygen  or  hydrogen. 

It  has  been  said  that  "matter  was  the  object  of  Chemistry," 
"  motion  of  Natural  Philosophy ;"  but  this  is  true  only  in  a  gen- 
eral sense.  Matter,  as  well  as  motion,  is  the  subject  of  investi- 
gation in  the  latter  science ;  not  its  composition,  but  its  consti- 
tution, form,  and  mass. 

The  science  of  Chemistry  may  be  included  in  a  few  fundament- 
al ideas  connected  with  changes  produced  by  the  force  of  affinity 
among  the  atoms  of  different  kinds  of  matter. 

The  science  of  Natural  Philosophy  may  also  be  embraced  in 
a  few  simple  ideas,  connected,  not  with  atoms  simply,  but  with 
changes  which  collections,  or  masses  of  matter,  undergo  under  the 
influence  of  certain  forces  yet  to  be  mentioned.  These  ideas  may 
be  expressed  by  a  few  terms,  by  means  of  which,  when  thoroughly 
comprehended,  nearly  all  the  facts  in  natural  philosophy  may  be 
explained.  Most  of  these  facts  may  be  referred  to  four  funda- 
mental ideas. 

1.  The  Idea  of  Matter,  which  arises  from  a  perception  of  ex- 
tension, that  is,  the  property  of  being  extended  in  space,  having 
length,  breadth,  and  thickness.  As  every  portion  of  matter,  how- 
ever small,  has  these  three  dimensions,  we  may  view  a  mass  of 
matter  as  a  collection  of  atoms,  which  are  incapable  of  being  di- 
vided, each  one  of  which  fills  a  separate  space,  and  of  necessity 
excludes  for  the  time  every  other  atom  from  the  space  which  it 

What  is  the  distinction  between  cohesion,  gravitation,  and  affinity? 
How  many  fundamental  ideas  include  most  of  the  facts  in  Natural  Philos 
ophy  ?  From  what  does  the  idea  of  matter  arise  ? 


INTRODUCTION.  15 

occupies.     The  idea  of  matter,  then,  may  be  expressed  by  the 
term  atom. 

A  collection  of  atoms  is  called  a  mass  or  body. 

2.  The  Idea  of  Force,  which  arises  from  change  of  place  or 
form.     This  force  either  exists  in  matter  or  is  exerted  upon  it, 
and  produces,  or  has  a  tendency  to  produce,  motion  or  a  change 
of  motion. 

When  force  exists  among  atoms,  and  tends  to  draw  them  to- 
gether, it  is  expressed  by  the  term  attraction,  of  which  there  are 
several  kinds. 

When  the  force  existing  among  atoms,  or  applied  to  them, 
tends  to  separate  them  from  each  other,  it  may  be  described  by 
the  term  repulsion,  a  force  supposed  to  be  due  to  caloric. 

When  the  force  arises  from  the  resistance  which  an  atom  or  a 
mass  opposes  to  a  change  of  state,  either  of  motion  or  of  rest,  it  is 
called  the  force  of  inertia. 

3.  The  Idea  of  Law. — A  clear  conception  of  forces  leads  di- 
rectly to  the  idea  of  the  laws  by  which  their  action  is  governed. 
By  the  laws  of  nature  are  meant  the  uniform  modes  in  which  the 
forces  of  nature  exert  their  powers.     A  law,  then,  is  a  uniform 
mode  of  action.     The  fact  that  under  the  same  circumstances 
the  same  effects  ensue,  is  denominated  a  law  of  nature.     Thus 
we  speak  of  gravity  as  the  force  which  retains  the  planets  in 
their  orbits,  but  the  laws  of  gravitation  are  the  uniform  modes  by 
which  this  force  is  exerted.     One  of  these  laws  is,  that  the  in- 
tensity of  the  force  decreases  as  the  square  of  the  distance  in- 
creases ;  that  is,  at  twice  the  distance,  two  bodies  will  attract 
each  other  with  but  one  fourth  the  power.    A  law,  then,  is  nothing 
more  than  a  general  truth  in  nature,  including  many  that  are 
minor  and  subordinate.     Thus,  for  example,  the  law  of  gravity 
extends  to  matter  under  every  form  and  throughout  all  space ; 
to  bodies  in  the  heavens  and  to  masses  near  the  earth.     It  is 
therefore  a  general  truth. 

4.  The  Idea  of  Design  or  Utility. — Our  investigations  of  mat- 

From  what  does  the  idea  of  force  arise  ?  What  names  are  given  to  the 
several  forces  of  nature  ?  What  is  the  third  idea,  and  from  what  do  we 
derive  it?  Meaning  of  law,  law  of  nature,  &c.  What  is  meant  by  de- 
sign or  utility  ? 


16  INTRODUCTION. 

ter,  its  forces  and  laws,  do  not  attain  their  highest  importance 
and  significance  until  we  reach  their  grand  purpose  and  design — 
until  we  are  able,  not  only  to  understand  the  uses  to  which  they 
may  be  applied,  which  opens  to  us  the  whole  field  of  the  useful 
and  ornamental  arts,  but  also  clearly  to  perceive  the  great  plan 
and  purpose  of  God  in  the  material  universe,  thus  enabling  us  to 
rise  above  these  material  forms  to  their  great  Author,  in  whom 
resides  all  power,  and  from  whom  all  forces  and  laws  proceed. 

If,  therefore,  the  student  will  fully  comprehend  what  is  meant 
by  the  terms  atom,  attraction,  repulsion,  inertia,  force,  law,  and 
purpose  or  utility,  he  will  be  able  to  explain  most  of  the  phe- 
nomena of  nature,  and  to  understand  those  processes  of  art  which 
belong  to,  or  are  connected  with,  the  science  of  Natural  Philos- 
ophy. 

In  addition  to  Chemistry  and  Physics,  or  Natural  Philosophy, 
there  is  another  branch  of  natural  science,  called 

Natural  History,  which  includes  a  classification  and  history 
of  all  natural  objects,  mineral,  vegetable,  and  animal.  The  nat- 
ural history  of  simple  minerals  constitutes  the  science  called  Min- 
eralogy ;  of  rocks,  or  the  crust  of  the  earth,  Geology  ;  and  of  ani- 
mals and  vegetables,  Biology  (or  science  of  life),  including  Bota- 
ny, the  natural  history  of  plants,  and  Zoology,  a  similar  history 
of  animals.  It  is  the  province  of  Natural  History  to  describe 
particular  bodies,  and  arrange  them  in  groups  or  classes.  It  is 
restricted,  however,  to  the  phenomena  of  perceptible  distance. 


DIVISION  OP  THE  SUBJECT. 

The  term  Physics  is  sometimes  used  instead  of  Natural  Phi- 
losophy. The  expression  Mechanical  Philosophy,  too,  some- 
times designates  the  same  science. 

That  part  of  Physics  which  relates  to  the  mechanical  proper- 
ties of  solids  is  called  Mechanics.  That  which  relates  to  the 


What  terms  must  be  clearly  understood  in  order  to  gain  a  correct  knowl- 
edge of  Natural  Philosophy?  Meaning  of  Physics.  Define  the  different 
branches  of  Natural  Philosophy.  Mention  the  different  branches  of  Nat- 
ural History; 


INTRODUCTION.  17 

equilibrium  and  motion  of  liquids  is  called  Hydrodynamics*  a 
term  including  Hydrostatics  and  Hydraulics.  That  which 
treats  of  the  mechanical  properties  of  air  and  other  gases  has 
received  the  name  of  Pneumatics.  It  is  thus  that  the  three 
forms  of  matter  furnish  the  foundation  for  this  threefold  division. 
But  there  are  other  branches  of  the  subject,  viz.,  Undulations, 
which  relate  to  water-waves,  waves  of  sound,  music,  &c.,  and 
Electricity,  Magnetism,  Light,  and  Heat.  The  four  last-men- 
tioned terms  designate  powers  or  forces  of  nature,  and  are  called 
imponderable  agents.  The  subject  of  heat  or  caloric  is  generally 
assigned  to  the  science  of  Chemistry,  but  the  others,  in  consequence 
of  their  giving  rise  to  the  phenomena  of  perceptible  motion,  come 
properly  into  the  province  of  Natural  Philosophy. 

Astronomy  is  also  another  branch,  though  frequently  regarded 
as  a  separate  science  ;  but  as  it  is  in  the  motions  of  the  heaven- 
ly bodies  alone  that  the  great  doctrines  of  Physics  find  their 
highest  and  truest  exemplifications,  Astronomy,  for  this  reason, 
is  a  most  important  branch  of  Natural  Philosophy. 

*  By  some  writers  Mechanics  is  divided  into,  1.  Statics,  which  treats  of 
the  equilibrium  of  solids;  2.  Dynamics,  which  treats  of  the  effects  offerees 
on  solids  when  motion  is  produced;  3.  Hydrostatics,  which  treats  of  the 
equilibrium  of  fluids ;  and,  4.  Hydrodynamics,  which  treats  of  the  motion 
of  fluids. 


NATURAL  PHILOSOPHY, 

CHAPTER  I. 

MATTER  AND  ITS  GOVERNING  FORCES. 
SECTION  I.— OF  MATTER. 

The  material  universe  is  made  up  of  very  minute  atoms,  each 
one  of  which  Jills  a  certain  portion  of  space,  and  though  fre- 
quently changing  its  position  in  reference  to  other  atoms,  is  in- 
capable of  being  annihilated,  unless  it  be  by  that  Power  which 
first  brought  it  into  being. 

THE  idea  of  matter  includes  at  least  the  perception  of  two 
properties,  Extension  and  Impenetrability.  By  extension  is 
meant,  that  every  particle  of  matter,  however  small  it  may  be 
conceived  to  be,  has  still  an  upper  and  an  under  surface,  or 
the  dimensions,  length,  breadth,  and  thickness.  The  capability 
which  a  mass  of  matter  has  of  being  divided,  is  called  the  prop- 
erty of 

1.  Divisibility. — The  extent  to  which  matter  is  susceptible 
of  division  is  not  known.  In  theory  it  is  indefinitely  divisible. 
Thus,  for  example,  if  a  silver  wire,  an  inch  in  length,  be  cut  in 
the  middle,  and  then  one  half  taken  and  divided  into  two  parts, 
and  the  process  of  halving  each  division  continued,  it  is  evident 
that  there  would  always  be  an  undivided  half,  at  whatever  point 
in  the  series  the  process  should  be  arrested.  We  should  have  a 
series  which  may  be  represented  by  the  fractions  {.,  i,  },  T\,  -^, 
^T,  &c.  Now,  you  might  multiply  the  denominators  of  the  frac- 
tions by  2,  or  halve  them  to  an  indefinite  extent.  Such  a  series 
would  never  terminate 

The  idea  of  matter  includes  the  perception  of  what  properties  ?  Divis- 
ibility of  matter,  how  illustrated  ? 


20  NATURAL    PHILOSOPHY. 

Or,  suppose  you  should  attempt  to  walk  out  of  your  house  by 
walking  one  half  the  way,  and  then  one  half  the  remaining  space, 
and  so  on,  it  is  evident  that  you  would  never  reach  the  threshold. 

In  practice,  we  should  soon  arrive  at  a  limit,  for  the  want  of 
mechanical  instruments  sufficiently  refined  to  carry  on  the  divis- 
ions ;  but  in  theory,  the  divisions  might  be  infinitely  extended. 
It  is  believed,  however,  that  there  is  a  limit  in  nature  to  this 
division,  and  that  we  should  finally  come  to  the  ultimate  atoms* 
or  molecules,  which  are  incapable  of  further  division,  being  abso- 
lutely hard  and  impenetrable. 

The  ultimate  atoms  of  matter  are  exceedingly  minute.  This 
is  shown  in  numerous  cases  in  which  division  has  been  carried  to 
such  an  extent  that  many  millions  of  them  in  a  mass  could  not 
be  seen  by  the  naked  eye.  Thus,  gold  leaf  .may  be  hammered 
to  the  •g-g-o^o'o^th  °^  an  *ncn  m  "thickness ;  and  if  silver  wire  be 
coated  with  gold,  it  may  be  drawn  out  to  such  an  extent  that 
the  thickness  of  the  gold  shall  be  a  thousand  times  less  than  the 
gold  leaf  itself.  A  grain  of  musk  will  send  off  particles  sufficient- 
ly numerous  to  fill  a  space  of  two  hundred  cubic  feet  every  day 
for  twenty  years,  without  losing  any  perceptible  weight.  The 
number  of  atoms  thus  diffused  exceeds  computation  or  expression  ; 
yet,  if  they  were  collected  and  placed  in  the  scale  of  a  delicate 
balance,  their  weight  could  not  be  appreciated.  The  thread  of 
the  spider's  web  is  so  attenuated  that  one  half  pound  of  it  would 
reach  around  the  globe  (25,000  miles),  and  five  pounds  would 
reach  to  the  moon,  a  distance  of  240,000  miles. 

Some  of  the  best  illustrations  of  the  extreme  minuteness  of  the 
atoms  of  matter  are  furnished  by  changes  in  liquids  and  gases. 

Experiment. — Take  one  gallon  of  water  colored  with  an  infusion  of  pur- 
ple cabbage,  and  put  into  it  a  single  drop  of  sulphuric  acid.  The  acid  will 
be  diffused  through  the  whole  quantity  of  the  water,  as  is  proved  by  the 
change  in  color.  A  drop  of  any  alkali  will  change  it  green. 

The  atoms  of  the  acid  and  of  the  alkali  must  be  diffused  through 
the  whole  mass  of  the  liquid  in  order  to  produce  the  effect.     The 
*  The  term  atom  means  that  which  is  incapable  of  being  cut  or  divided. 

Is  matter  indefinitely  divisible  ?  What  supposition  is  made  in  reference 
to  the  ultimate  atoms  ?  Can  we  ascertain  by  experiment  the  exact  size  of 
atoms  ?  What  facts  show  their  extreme  minuteness  ? 


DIVISIBILITY IMPENETRABILITY.  2 1 

evaporation  of  any  liquid,  by  which  it  takes  the  state  of  gas  or 
vapor,  also  illustrates  the  great  extent  to  which  this  division  must 
proceed.  But  perhaps  the  most  striking  example  is  in  the  animal 
kingdom,  in  the  case  of  those  infusorial  animals  which  are  found 
to  exist  in  all  solid  and  liquid  bodies,  and  throughout  the  regions 
of  the  atmosphere.  Many  millions  of  these  animals  would  not 
exceed  a  grain  of  sand  in  bulk,  and  yet  they  have  a  very  compli- 
cated organization  ;  a  stomach,  organs  of  respiration,  circulation, 
&c.  The  blood  vessels  of  these  animals  are  very  minute  tubes, 
but  the  globules  of  blood  would  seem  to  be  well-nigh  elementary 
atoms,  and  yet  blood  is  a  complex  body,  the  smallest  globule  of 
which  contains  seventy-five  elementary  atoms.  To  such  minute- 
ness must  the  division  of  matter  be  carried  in  the  several  exam- 
ples above  referred  to,  that  the  thought  has  often  been  suggested 
that  the  ultimate  atoms  are  nothing  but  the  forces  of  nature,  act- 
ing in  determinate  directions,  and  producing  what  we  call  matter. 
This  idea,  however,  can  not  be  received,  for  it  is  evident  that  each 
of  these  atoms,  however  minute  they  may  be,  must  have  the  other 
property  of  a  mass. 

2.  Impenetrability. — Not  that  we  are  ever  able  to  arrive  at 
the  ultimate  atom  and  try  the  experiment  upon  it,  but  we  are 
able,  by  various  experiments  and  from  facts  in  nature,  to  prove 
that  every  atom  must  occupy  a  portion  of  space,  and  exclude  for 
the  time  any  other  atom  from  it ;  for  it  is  obvious  that  a  col- 
lection, of  atoms  can  not  occupy  a  large  space,  if  one 
single  atom  does  not  occupy  a  small  portion  of  it. 

The  impenetrability  of  matter  may  be  proved  by 
experiment,  and  illustrated  by  many  familiar  phe- 
nomena of  nature  and  art. 

Exp. — Place  a  lighted  taper,  attached  to  a  piece  of  cork, 
a,  Fig.  1,  on  water  contained  in  a  deep  glass  vessel.  Place 
over  it  a  tubulated  receiver,  b,  and  press  it  down.  The  taper 
will  be  carried  down  apparently  into  the  water,  showing  that 
the  air  which  is  in  the  receiver  will  not  permit  the  water  to 
take  its  place.  If  now  the  stop-cock,  c,  be  turned,  the  air 
will  escape,  the  water  will  rush  in  to  fill  its  place,  and  the 
taper  will  apparently  rise  out  of  the  water.  This  is  the  prin- 

What  examples  of  the  minuteness  of  atoms  are  most  remarkable  ?  What 
is  meant  by  impenetrability  ?  What  experiments  prove  the  impenetrabili- 
ty of  matter  ? 


22  NATURAL    PHILOSOPHY. 

ciple  of  the  diving  bell,  the  taper  representing  the  man  and 
the  receiver  the  bell. 

A  funnel  or  a  glass  tube,  a,  Fig.  2,  will  also  show  the  same 
fact. 

Exp. — Place  your  finger  upon  the  open  end  of  the  funnel, 
and  attempt  to  force  it  into  the  water;  the  air  will  exclude 
the  water,  but,  on  removing  your  finger,  the  air  will  rush  out 
and  the  water  will  rise  to  the  same  level  within  as  without  the 
vessel^ 

By  these  and  other  experiments  it  is  demonstrated 
that  gases  and  liquids  can  not  be  made  to  penetrate 
each  other.  Therefore,  the  presence  of  the  one  neces- 
sarily excludes  the  other  from  the  space  it  occupies. 

Numerous  illustrations  of  the  same  fact  are  constantly  occur- 
ring in  nature  and  in  art.  Two  solid  bodies  can  not  be  forced 
into  each  other  by  any  known  mechanical  power.  A  nail  is 
driven  into  wood,  but  it  only  displaces  the  particles  of  the  wood. 
The  same  is  true  in  all  other  cases.  We  can  not  force  a  solid 
piston  into  the  barrel  of  a  pump  if  there  is  water  below  it.  When 
a  solid  is  thrown  into  water,  it  separates,  but  does  not  penetrate 
the  water.  The  same  is  true  of  solids  pressing  through  air  ;  the 
particles  of  air  are  separated,  but  not  penetrated ;  for  if  air  be 
contained  in  a  cylinder,  and  a  solid  piston  introduced,  no  power  is 
sufficient  to  force  it  to  the  bottom.  This  is  illustrated  by  the 
fire-syringe.  Hence  it  is  manifest  that  every  atom  of  matter  has 
the  property  of  excluding  every  other  from  the  space  it  occupies, 
and  has,  therefore,  a  veritable  existence. 

Is  it  possible  to  destroy  an  atom  of  matter  ? 

If  the  ultimate  particles  can  not  be  further  separated  by  me- 
chanical means,  we  should  infer  that  their  annihilation  was  im- 
possible. Hence  a  third  property  of  matter  is 

3.  Indestructibility. — A  mass  of  atoms  may  be  separated  and 
changed  from  one  form  to  another  by  chemical  and  mechanical 
forces,  but  not  one  of  them  can  ever  be  lost ;  for  in  all  cases 
where  a  body  is  apparently  destroyed,  it  can  be  shown  experi- 
mentally that  the  parts  are  only  separated,  and  can  be  collected 
again.  Thus,  when  wood  is  burned  in  the  fire,  it  appears  to  be 

Difference  between  penetrating  and  separating  the  atoms  of  matter. 
Can  matter  be  destroyed  ?  What  becomes  of  wood  when  it  is  burned  in 
the  fire? 


INDESTRUCTIBILITY    OP    MATTER.  23 

annihilated  ;  but  if  we  collect  the  products — the  smoke  and  ash- 
es, we  shall  find  the  same  quantity  in  weight  that  existed  in  the 
wood.  In  fact,  we  shall  find  a  larger  amount  of  matter  than 
was  originally  contained  in  the  wood,  owing  to  the  oxygen  of  the 
air  which  has  combined  with  the  wood  in  the  process  of  com- 
bustion. 

When  gunpowder  is  exploded,  the  products  may  all  be  collect- 
ed again. 

The  same  is  found  true  in  every  case  where  matter  changes  its 
form  or  composition.  We  know  that  the  material  atoms  of  our 
own  bodies  are  constantly  changing,  but  not  one  of  them  is  ever 
annihilated.  That  atom  of  matter  which  was  struck  from  its 
kindred  particles  ages  since,  may  have  passed  through  many 
forms,  solid,  liquid,  and  gaseous,  perhaps  through  animal  and 
vegetable  bodies,  before  it  entered  the  kernel  of  grain,  and  became 
a  portion  of  our  own  system  ;  and  there  are  many  changes  which 
it  will  undergo  there  before  it  shall  be  cast  out  into  the  air  as 
pure  as  at  first,  to  enter  other  forms  and  nourish  other  systems. 
Matter  is  thus  ever  changing,  but  never  destroyed.  In  saying 
that  matter  is  indestructible,  it  is  simply  meant  that,  as  far  as 
our  observation  goes,  and  by  means  of  the  powers  we  are  able  to 
exercise  upon  it,  it  is  so.  It  is  not  pretended  to  decide  whether 
He  who  formed  matter  may  not  also  destroy  it. 

We  are  to  conceive  of  the  material  universe  as  made  up  of 
atoms,  and  our  idea  of  matter  is  an  idea  of  one  of  these  atoms 
exceedingly  minute,  incapable  of  further  division,  absolutely  hard, 
excluding  every  other  atom  from  the  space  itself  occupies,  and, 
though  constantly  changing  its  position  in  reference  to  other  at- 
oms, incapable  of  annihilation  exceprt  by  the  hand  of  God. 

What  changes  are  taking  place  in  the  human  system?  How  much  is 
implied  in  saying  that  matter  is  indestructible  ? 


24  NATURAL  PHILOSOPHY. 


SECTION  II.— OF  THE  FORCES  WHICH  GOVERN  MATTER  AND  THE  PROP 
ERTIES  RESULTING  THEREFROM. 

Material  atoms  are  subjected  to  certain  forces,  called  Attrac- 
tion, Repulsion,  and  Inertia,  which  give  rise  to  the  most  import- 
ant properties  of  matter  in  masses. 

I.  Attraction  is  of  various  kinds,  such  as 

I.  Cohesion,  which  holds  the  atoms  of  solids  and  liquids  to- 
gether, and  which,  being  opposed  by  the 

Repulsion  of  heat  or  caloric,  gives  rise  to  the  three  forms  of 
matter,  solid,  liquid,  and  gaseous,  and  to  that  crystalline  struc- 
ture which  matter  is  universally  disposed  to  assume  ;  also  to  the 
properties  of  hardness,  density,  elasticity,  porosity,  tenacity,  and 
the  like.  2.  Capillary  Attraction,  which  takes  place  between 
solids  and  liquids.  3.  Electrical  and  Magnetic  Attraction. 
4.  Chemical  Affinity ;  and,  5.  Attraction  of  Gravitation. 

II.  Matter  also  possesses  the  force  of  Inertia,  which  is  a  re- 
sistance to  motion,  or  to  a  change  of  motion  in  bodies. 

THERE  are  three  generic  forces  which  govern  matter,  Attrac- 
ti&n,  Repulsion,  and  Inertia.  The  form  which  matter  assumes 
and  some  of  its  properties  depend  upon  their  action. 

I.  Attraction  and  Repulsion. — If  there  were  but  one  atom  in 
the  universe,  it  would  remain  in  the  state  in  which  it  might 
chance  to  be  placed.  But  if  another  atom  were  introduced, 
there  would  spring  up  between  them  a  mutual  attraction,  and, 
unless  otherwise  prevented,  they  would  move  toward  each  other. 
This  property  is  called  attraction,  of  which  there  are  several  kinds. 
Their  actual  contact,  however,  would  be  prevented  by  a  force  of 
repulsion  which  surrounds  each  atom  of  matter,  so  that  no  force 
is  sufficient  to  cause  the  atoms  in  a  solid  block  to  touch  each  other. 

1 .  As  the  atoms  which  compose  a  block  adhere  to  each  other 
and  require  force  to  separate  them,  it  is  evident  there  must  be 
some  force  residing  in  the  atoms  themselves  to  cause  this  adhe- 
sion, and  which  must  be  overcome  when  the  particles  are  separ- 
ated. This  force  is  called  the  attraction  of 

What  are  the  forces  which  govern  matter  ?     Define  attraction. 


ATTRACTION    OF   COHESION. 


25 


Cohesion  or  Aggregation. — It  is  exerted  only  when  the  atoms 
are  so  exceedingly  near  each  other  as  to  be  brought  into  ap- 
parent contact ;  and  the  only  reason  why  this  force  is  not  al- 
ways exhibited  whenever  two  solid  bodies  are  brought  near 
each  other  is,  that  the  roughness  of  the  surface  prevents  the 
particles  from  coming  sufficiently  near  to  be  brought  under  its 
influence. 

If  two  solids  be  made  very  smooth  by  polishing  their  sur- 
faces, and  then  be  pressed  together,  they  will  cohere  with  great 
force.  , 

?. — Take  two  bars  or  balls  of  lead,  Fig.  3,  and  scrape  their  surfaces 
smooth  with  a  sharp  knife,  and  then 
press  them  together;    it  will  require 
a  force  of  several  pounds  to  separate 
them.     If  the  surfaces  could  be  made 
r/'  perfectly  smooth,  the  bars  would  sepa- 
rate in  any  other  place  as  readily  as  at 
the  point  where  they  are  joined. 

Exp. — Take  a  piece  of  India  rubber,  and  cut  it  in  two  pieces  with  a  sharp 
knife.  On  applying  the  surfaces  of  the  severed  parts  they  will  cohere  with 
nearly  the  same  force  that  they  did  before  they  were  separated. 

The  cohesion  between  a  solid  and  a  liquid  may  be  shown  by 
taking  pieces  of  glass  or  wood,  and 
suspending  them  from  the  end  of  a 
balance,  Fig.  4,  so  that  the  flat  sur- 
face of  the  glass  may  touch  the  sur- 
face of  the  water,  b.  By  applying 
weights  in  the  other  scale,  the  exact 
force  of  cohesion  may  be  determined. 
This  is  sometimes  called  the  force 
of  adhesion,  and  is  found  to  be  con- 
siderable, depending  upon  the  extent 
of  surface. 

When  the  glass  is  removed  a  film  of  water  adheres  to  its  sur- 
face, showing  that  the  separation  does  not  take  place  between  the 
water  and  glass,  but  that  the  particles  of  water  are  separated. 
This  experiment  also  proves  that  the  particles  of  water  attract 
each  other.  If  the  force  of  adhesion  is  greater  than  that  exist- 
ing between  the  particles  of  the  liquid,  the  liquid  will  adhere  to 

Cohesion.  Why  do  not  all  bodies  cohere  when  they  meet  each  other? 
Experiment  of  lead  balls — India  rubber.  How  may  the  attraction  be- 
tween solids  and  liquids  be  shown  1  Which  is  greater,  the  attraction  be- 
tween the  liquid  and  solid,  or  between  the  particles  of  the  liquid  1 

B 


Fig.  4. 


26  NATURAL    PHILOSOPHY. 

the  body  and  wet  it.  If  it  be  less,  the  liquid  will  not  adhere  to 
it.  The  power  of  cohesion  among  the  particles  of  liquids,  how- 
ever, is  very  small  compare^  with  that  between  the  particles  of 
solids.  The  fact  that  a  small  quantity  of  any  liquid  assumes  a 
globular  form,  as  in  drops  of  water  or  mercury,  is  further  proof 
that  cohesion  exists  to  a  certain  extent,  though  their  particles 
are  so  far  removed  from  each  other  that  the  force  is  slight. 

Gaseous  bodies  seem  to  be  destitute  of  this  power,  because  their 
particles  are  removed  beyond  the  reach  of  each  other's  attraction. 
There  is,  however,  a  strong  attraction  between  some  solids  and 
gases,  and  also  between  liquids  and  gases.  Charcoal  and  many 
porous  bodies  will  absorb  many  times  their  volume  of  several 
gases,  as  ammonia,  watery  vapor,  &c.  Water  always  contains 
air  and  other  gases,  which  it  absorbs  in  greater  or  less  quanti- 
ties, according  to  the  nature  of  the  gas,  the  time  of  exposure,  and 
degree  of  pressure.  Hence  the  force  of  cohesion  is  strongest  in 
solids  ;  in  liquids  it  is  slight,  and  in  gases  it  is  wholly  inoperative. 
The  explanation  of  the  different  degrees  of  cohesion  among  the 
atoms  of  matter  is  found  in  the  action  of  an  antagonistical  force 
called 

Repulsion,  or  the  Force  of  Caloric. — When  heat  is  applied 
to  any  solid  body,  it  expands  it,  and  the  higher  the  temperature 
is  raised,  the  greater  will  the  increase  of  volume  become  for  equal 
additions  of  heat,  until  at  a  certain  temperature  the  solid  becomes 
liquid,  or  melts.  In  such  cases  the  cohesion  is  mostly  overcome 
by  the  repulsive  tendency  of  heat ;  the  particles  become  removed 
beyond  the  reach  of  their  mutual  attraction,  and  thus  separate. 

If  the  heat  be  continued,  most  liquid  bodies  may  have  their 
cohesion  entirely  overcome,  and  be  made  to  assume  the  state  of 
gas  or  vapor.  Now  the  moment  that  the  change  takes  place 
from  a  solid  to  a  liquid,  or  from  a  liquid  to  a  gas,  a  large  quantity 
of  heat  is  absorbed  by  the  body,  or  passes  into  an  insensible  state. 
This  heat  is  given  out  again  when  the  body  is  condensed,  and  re- 
turns to  the  liquid  or  solid  form. 

Hence  it  is  inferred  that  the  three  forms  of  matter,  solid,  liq- 

Cohesiou  of  solids,  liquids,  and  gases  compared.  What  constitutes  the 
difference  ?  What  force  opposes  cohesion  ? 


CRYSTALLINE    FORMS.  27 

uid,  and  gaseous,  are  due  to  the  different  quantities  of  caloric 
existing  among  their  atoms. 

This  heat,  however,  does  not  affect  the  thermometer.  It  is 
the  caloric  of  fluidity  and  of  gases.  Thus,  for  example,  water 
at  a  certain  temperature  is  in  a  state  of  gas,  in  which  state  it 
contains  a  thousand  degrees  of  heat,  which  is  insensible  to  the 
thermometer,  and  which  must  be  abstracted  before  it  can  assume 
the  liquid  form.  Water  in  its  liquid  form  contains  a  quantity  of 
heat  (140°),  which,  at  the  moment  it  freezes,  must  be  given  out, 
or  it  will  not-  become  solid. 

The  different  forms  of  matter,  therefore,  depend  upon  the  rel- 
ative intensity  of  cohesion,  and  of  heat,  or  repulsion.  In  solids, 
cohesion  preponderates  ;  in  liquids  there  seems  to  be  a  balance 
of  powers,  but  in  gases  caloric  has  entirely  overcome  the  cohesive 
force,  by  removing  the  atoms  beyond  the  influence  of  their  mu- 
tual attractions. 

When  gases  or  liquids  pass  to  the  solid  state,  they  are  disposed 
to  assume  definite  forms,  called 

Crystalline  Forms. — This  seems  due  to  a  peculiar  action  of 
cohesion.  If  we  suppose  that  the  atoms  are  like  magnets,  that 
is,  that  they  have  two  points  which  have  the  power  of  attraction, 
so  that  they  will  form  themselves  into  rows  in  definite  directions, 
all  other  points  being  destitute  of  attractive  power,  we  may  ac- 
count for  the  forms  which  matter  is  thus  universally  inclined  to 
assume. 

The  crystalline  forms  which  different  bodies  assume  are  quite 
uniform  for  the  same  kind  of  matter,  and  from  the  shape  of  the 
crystal  we  may  perhaps  infer  the  shape  of  the  atoms  which  com- 
pose it. 

SJiape  of  Atoms. — The  shape  of  atoms,  however,  must  be  a 
matter  of  conjecture.  They  are  generally  considered  to  be  either 
spheres  or  spheroids.  If  we  suppose  the  atoms  of  cubes  and  all 
rectangular  solids  to  be  spheres,  it  is  easy  to  account  for  these 
forms ;  thus, 

The  different  forms  of  matter  are  due  to  what  circumstance  ?  What 
forces  appear  to  act  in  opposition  to  each  other?  What  forms  are  gases 
and  liquids  disposed  to  assume  when  they  pass  to  the  solid  state  ?  From 
what  may  we  infer  the  shape  of  atoms  ? 


28 


NATURAL    PHILOSOPHY. 


Let  A,  Fig.  5,  represent  a  number  of  atoms  of  a  liquid.     Now, 
when  this  liquid  crystallizes  in  the 
form  of  a  cube,  each  of  the  atoms  is 

supposed  to   assume  a  polarity,  and  ^-Q-VV  ^HEES^oJGh Ji- 

tney arrange  themselves  as  in  B,  there 
being  two  axes  of  attraction  at  right 
angles  to  each  other,  as  e  d,  i  n,  &c. 
A  great  many  forms  may  be  made 
out  by  changing  the  direction  which  the  two  axes  bear  to  each 
other.  B,  however,  represents  only  one  face  of  the  cube. 

If  the  atoms  are  spheroids,  that  is,  egg-shaped,  then  it  will  be 
evident,  by  inspecting  the  figure,  that  a  great  variety  of  crystalline 
forms  may  result  from  a  change  in  the  direction  of  the  polarizing 
axes. 

Thus  the  axes  might  be  varied  indefinitely.  Fig.  6,  A,  B,  C,  D, 
exhibits  four  forms.  Fig.  6. 

These    different    di-      A  B 

rections  of  the  axes, 
and  there  are  gener- 
ally three  or  more 
axes,  would  give  rise  to  almost  any  conceivable  form  of  crystal. 
It  is  true  the  molecule  or  atom  may  have  the  same  form  as  the 
crystal  itself,  but  the  sphere  and  spheroid  are  the  most  simple,  and 
enable  us  to  account  for  all  the  fo^ms  which  matter  assumes.* 

When  a  body  crystallizes,  as  when  water  freezes,  it  generally 
expands,  in  consequence  of  the  different  arrangement  of  its  atoms 
requiring  more  space  than  formerly.  This  is  seen  in  Fig.  5,  A,  B. 

It  is  owing  to  this  fact,  and  to  the  repulsive  tendency  of  heat, 
together  with  what  may  be  called  the  natural  repulsion  of  atoms, 
that  a  mass  of  atoms  always  has  the  property  called 

(1.)  Porosity. — If  the  atoms  of  which  a  mass  is  composed  were 
round  or  spheroidal,  there  would  naturally  be  spaces  between 
them,  even  if  there  were  no  repulsive  power  to  separate  them 
from  each  other,  and  this  property  of  porosity  would  result  directly 
from  the  shape  of  the  atoms  ;  but  when  we  add  the  repulsion 
of  heat  and  the  polarity  of  the  atoms,  we  can  easily  see  how  all 
*  See  J.  D.  Dana  on  Cohesive  Attractiop,  Silliman's  Journal,  Nov.,  1847 


How  may  the  different  forms  of  crystals  be  accounted  for  ?     What  is  tha 
most  probable  shape  of  atoms  ?     What  does  porosity  result  from  ? 


POROSITY ELASTICITY.  29 

matter,  however  dense  it  may  be  to  appearance,  is  yet  filled  with 
pares. 

This  property  may  easily  be  seen  by  aid  of  the  microscope,  or 
by  very  simple  experiments  in  relation  to  most  organic  bodies, 
but  in  the  more  dense  bodies,  as  gold  and  platinum,  the  existence 
of  pores  is  not  so  easily  demonstrated. 

In  the  famous  Florentine  experiment,  water  was  forced  by  great 
pressure  through  the  substance  of  a  hollow  gold  ball  in  such  quan- 
tities that  it  oozed  in  drops  from  the  outer  surface.  Many  solid 
bodies,  such  as  crystalline  stones,  sugar,  &c.,  will  absorb  c'onsid- 
erable  quantities  of  water,  which  proves  them  to  be  porous. 

But  the  best  examples  are  found  in  the  animal  and  vegetable 
world.  The  pores  in  bone  and  wood  are  easily  seen  by  the  na- 
ked eye.  With  the  aid  of  the  microscope,  they  appear  like  large 
tubes  running  lengthwise  through  the  bone  or  wood.  The  po- 
rosity of  wood  is  beautifully  exhibited  in  what  is  called  the 
Air  Shower. 

Exp. — A  solid  piece  of  wood,  a,  Fig.  7,  is  fitted  to  the  receiver,  c,  of  an 
air  pump,  with  one  end  inserted  in  a  vessel  of  water,  b.  On 
exhausting  the  air  from  the  receiver,  the  external  air  will 
press  through  the  pores  of  the  wood,  from  a  to  b,  and  rise  up 
in  bubbles  through  the  water. 

It  is  more  difficult  to  show  the  pores  in  liquids 
and  gases,  but  they  must  exist  in  much  greater  mag- 
nitude than  even  in  solids,  as  is  evident  from  the 
fact  that  some  liquids  and  all  gases  and  vapors  occu- 
py more  space  than  when  in  the  solid  state. 

In  consequence  of  the  repulsion  existing  among 
the  particles  of  bodies,  and  also  because  of  the  shape 
and  position  of  the  atoms,  there  arises  another  property  called  , 
(2.)  Elasticity. — In  some  solid  bodies  the  particles  are  so  sit- 
uated as  to  yield  to  any  force  to  a  certain  extent,  and  then  return 
to  their  former  position.  This  is  exemplified  in  the  case  of  steel 
springs,  glass,  marble  balls,  ivory,  India  rubber,  and  many  other 
substances.  The  degree  of  elasticity  varies  in  different  bodies. 

How  is  this  property  shown  ?  What  are  the  best  examples  of  porosity  ? 
Illustrate.  From  what  is  elasticity  derived  ?  Define  what  the  property 
is.  How  does  it  vary  in  different  bodies  ? 


30  NATURAL    PHILOSOPHY. 

The  particles  of  some  "bodies  may  be  removed  very  far  from  each 
other  without  being  thrown  out  of  the  sphere  of  their  mutual  at- 
traction. 

The  celebrated  blade  of  Damascus  can  be  bent  double  without 
breaking,  while  some  bodies  break  with  the  least  jar. 

Hard  bodies  are  generally  elastic,  and  in  most  cases  regain 
their  form  when  subjected  to  a  momentary  pressure  ;  but  if  any 
solid  body  be  subjected  to  a  pressure  for  a  long  time,  it  gradually 
loses  its  power  to  spring  back  to  its  original  form.  It  is  probable, 
in  this  case,  that  some  change  may  take  place  in, the  direction 
of  the  cohesive  force  as  respects  the  molecules  of  which  the  body 
is  composed.  Thus,  a  spring  or  marble  slab,  when  bent  for  a 
long  time,  at  length  retains  the  impression,  and  becomes  perma- 
nently crooked. 

Liquids  are  much  more  elastic  than  solids  ;  when  subjected  to 
pressure,  they  yield  with  difficulty,  but  return  to  their  former 
volume  when  the  pressure  is  removed. 

Gases,  such  as  air,  are  perfectly  elastic  ;  that  is,  when  a  given 
portion  is  compressed,  it  returns  to  its  former  bulk  in  all  cases, 
unless  condensation  takes  place,  and  the  gas  changes  its  form  and 
becomes  a  liquid.  This  is  exemplified  in  pressing  a  gas  bag  or 
bladder  filled  with  air.  Gases  are  distinguished  from  solids  and 
liquids  by  the  greater  extent  of  their  elasticity,  and  this  is  due  to 
the  absence  of  cohesion ;  the  particles,  being  left  to  move  with 
the  greatest  freedom  upon  each  other,  are  held  together  by  grav- 
itation, or  their  weight  alone.  Elasticity  implies  another  prop- 
erty of  matter, 

(3.)  Compressibility,  by  which  is  meant  that  the  particles  in 
bodies  are  capable  of  being  compressed  into  smaller  spaces  than 
they  ordinarily  occupy.  Thus,  for  example,  the  atoms  of  solids, 
both  elastic  and  non-elastic,  may  be  made  to  approach  each  other 
by  pressure  or  hammering,  in  various  degrees  of  contiguity. 

Liquids  are  less  compressible  than  solids,  but  gases  possess 
this  property  in  the  highest  degree.  Air,  for  instance,  is  perfectly 

Do  bodies  ever  lose  their  elasticity  ?  What  bodies  are  most  elastic  ? 
How  do  liquids  compare  with  solids  ?  How  do  gases  compare  with  liquids 
and  solids  ?  What  is  meant  by  compressibility,  and  what  bodies  possess  it 
in  the  highest  degree  ? 


DENSITY HARDNESS.  31 

compressible  ;  twice  the  force  halves  the  volume  it  occupies.  It 
is  on  this  account  that  the  same  substance  may  be  made  to  occu- 
py less  space  ;  hence  arises  another  property, 

(4.)  Density,  which  has  reference  to  the  number  of  atoms  or 
quantities  of  matter  which  occupy  a  given  space.  If  we  suppose 
the  weight  and  proximity  of  atoms  in  any  two  bodies  to  vary,  it 
is  easy  to  see  that  the  one  may  be  more  dense  than  the  other. 

When  the  different  weights  of  equal  volumes  are  compared 
with  some  standard,  as  water  or  air,  density  becomes  specific 
gravity.  Of  course,  bodies  most  dense  have  the  greatest  specific 
gravity.  Hydrogen  is  the  lightest  body,  and  Platinum  the  heav- 
iest. We  do  not  know  how  dense  a  body  might  become,  were  its 
atoms  made  to  touch  each  other.  It  has  frequently  been  assert- 
ed, as  a  supposition  of  Newton,  that  "  if  the  matter  of  the  earth 
were  compressed  so  much  that  the  particles  should  touch  each 
other,  the  whole  might  not  exceed  a  cubic  inch  in  diameter," 
which,  if  not  an  absurd,  is  at  least  rather  an  extravagant  idea. 

There  are  several  other  properties  resulting  from  modifications 
of  the  cohesive  force,  as 

(5.)  Hardness,  which  might  be  supposed  to  result  from  dens- 
ity, but  this  is  not  always  the  case.  This  property  appears  to  de- 
pend upon  the  direction  of  the  axis  of  force  in  the  atoms  of  which 
different  bodies  are  composed,  so  that  the  particles  maintain  their 
position  with  great  fixedness  in  certain  directions.  The  diamond 
is  the  hardest  body  in  nature,  and  the  degrees  of  hardness  in  dif- 
ferent bodies  are  generally  determined  by  their  power  in  cutting 
and  scratching  other  bodies.  Some  bodies  become  hard  by  heat- 
ing, and  then  suddenly  cooling  them.  Such  is  the  fact  in  the 
operation  of  making  steel,  from  which  all  our  edged  tools,  and  a 
great  variety  of  machines  useful  in  the  arts,  are  produced. 

(6.)  Brittleness  is  still  another  property  of  matter.  A  brittle 
body,  such  as  glass  or  flint,  may  be  very  hard,  but  the  cohesion 
of  the  particles  is  such  that  a  slight  concussion  is  sufficient  to  sep- 
arate them. 

(7.)  Ductility  is  that  property  of  matter  by  which  it  is  capa- 

Describe  density,  specific  gravity,  and  hardness.  Describe  brittleness 
and  ductility. 


32  NATURAL    PHILOSOPHY. 

ble  of  being  drawn  out  into  wire.     Iron,  gold,  silver,  and  platinum 
are  very  ductile  substances. 

(8.)  Malleability  is  the  property  of  being  beaten  or  rolled  out 
into  thin  leaves.  Gold  is  the  most  malleable  of  all  bodies. 

(9.)  Pliability  is  the  name  given  to  the  ready  yielding  of  the 
particles,  as  in  elastic  bodies  ;  but  the  atoms  do  not  change  their 
places,  as  in  the  case  of  ductility. 

(1,0.)  Tenacity. — The  force  of  cohesion  varies  greatly  in  dif- 
ferent bodies,  and  is  the  cause  of  their  form  and  strength.  This 
cohesive  force  produces  the  property  of  tenacity,  by  which  is 
meant  the  force  by  which  the  parts  cohere  or  resist  a  steady  strain 
in  one  direction.  This  force  is  measured  by  the  power  required 
to  part  a  given  weight  or  volume  of  any  substance  in  the  form  of 
wire  or  cord.  Thus,  by  suspending  different  weights  to  several 
wires  of  the  same  size,  that  which  will  sustain  the  greatest  weight 
is  said  to  be  the  most  tenacious.  It  is  found  that  iron  and  steel 
are  most  tenacious.  If  iron,  copper,  gold,  and  oak  were  thus 
compared,  their  absolute  strength,  or  that  in  the  direction  of  their 
length,  would  be  as  the  respective  numbers  70,  19,  9,  12. 

Portions  of  the  animal  body  have  very  great  tenacity,  as  silk, 
wool,  hair,  animal  tendons,  and  portions  of  the  intestines,  which 
constitute  the  material  for  stringed  instruments,  as  the  harp  and 
violin.  Ships  are  now  made  of  iron,  and  bridges  are  suspended 
by  iron  wires.  It  is  one  of  the  most  important  objects  of  the 
engineer  and  architect  to  become  acquainted  with  the  relative 
strength  of  the  materials  which  he  wishes  to  use  in  the  construc- 
tion of  various  works  of  art. 

2.  Capillary  Attraction  takes  place  between  liquids  and  solids. 
When  a  solid  body  is  immersed  in  a  liquid,  Fig.  8. 

if  the  liquid  wets  the  body,  it  is  drawn  up- 
ward ;  if  it  does  not  wet  it,  a  depression 
takes  place.  Thus: 


Exp. — By  immersing  small  glass  tubes,  a,  Fig.  x\~ 
8.  in  any  liquid,  as  water,  the  liquid  will  rise  \\ 


higher  on  the  inside  of  the  tubes  than  on  the  out- 
side.    The  effect  is  rendered  more  perceptible  by  coloring  the  liquid. 

Describe  malleability,  pliability,  tenacity.  What  bodies  possess  these 
'properties  in  the  highest  degree?  How  is  the  tenacity  of  different  bodies 
ascertained  ?  Capillary  attraction.  Describe  and  illustrate  it. 


CAPILLARY    ATTRACTION. 


Fig.  10. 


If  the  tubes  are  of  different  diameters,  the  smaller  the  aper- 
ture of  the  tube^  the  higher  will  the  liquid  rise.  v  <?•*.•> 

Fig.  9.  Exp. — This  law  is  beautifully  illustrated  by  means 

of  two  pieces  of  glass,  Fig.  9,  joined  by  their  edg- 
es, b  c,  at  a  small  angle,  and  immersed  in  a  col- 
ored liquid.  The  different  heights  to  which  the 
liquid  will  rise  forms  a  curve,  a  b,  the  heights  de- 
pending upon  the  different  distances  the  two  plates 
are  from  each  other ;  hence,  when  water  is  contain- 
ed in  a  glass  vessel,  the  surface  is  not  level,  but  curves 
upward  where  it  touches  the  glass,  while  the  sur- 
face of  a  similar  vessel  of  mercury  curves  downward.. 
.  This  is  seen  in  A  B,  Fig.  10. 

It  is  due  to  this  figure  of  the  surface  that  float- 
-n  ing  solids  sometimes  move  toward  and  sometimes 
from  each  other,  a  phenomenon  often  ascribed  to 
attraction  and  repulsion.     Thus,  for  example  : 

Let  A  B,  Fig.  11,  be  two  balls  of  cork, 
or  some  light  substance.  If  they  are  oiled, 
so  that  the  water  will  not  wet  them,  there 
will  be  a  depression  around  them,  and  when 
they  approach  each  other,  the  water  at  C 
will  be  repelled,  and  they  will  fall  together ; 
^^^^^  or,  if  both  are  wet,  they  will  also  approach 

each  other,  because  the  elevation  between  them  will  be  less  than 
that  around  them.  If  one,  D,  is  wet,  and  the  other,  E,  oiled, 
the  water  will  be  elevated  around  D  and  depressed  around  E ; 
hence  they  will  seem  to  repel  each  other. 

If  the  tubes  are  immersed  in  mercury,  there  will  be  a  depres- 
sion of  the  metal  around  the  inner  surface.     When  the  liquid 
rises  the  bounding  surface  is  concave,  and  when  it  sinks  it  is  convex. 
It  is  due,  also,  to  capillary  attraction  that  the  fluids  of  animals 
Fig.  12.       and  vegetables  are  carried  through  many  portions  of 
their  substance.     All  vegetable  and   animal  tissues 
consist  of  bundles  of  tubes,  which  continually  absorb 
and  circulate  their  liquids  with  an  astonishing  force. 
This  fact  may  be  mechanically  illustrated  by  means 
of  a  bladder  tied  over  one  end  of  a  glass  tube  or  cup- 
ping-glass.   If  the  tube  with  the  bladder  be  immersed 
in  a  vessel  of  water,  B,  as  represented  m  Fig-.  12, 

Is  the  surface  of  water  or  of  mercury  in  a  vessel  le-»l?  Why  are  they 
not  ?  Why  do  floating  bodies  sometimes  approacl  and  at  others  recede 
from  each  other  ? 

B2 


34  NATURAL    PHILOSOPHY. 

and  then  filled  with  alcohol  to  the  same  height  of  the  water,  «, 
in  a  vftry  short  time  the  liquid  will  rise  in  the  tube  to  d,  and 
even  to  the  height  of  thirty  inches  or  more.  The  bladder  is  full 
of  small  tubes,  and  the  water  is  forced  in  while  a  small  quantity 
of  the  alcohol  flows  out.  The  internal  flow  was  called  by  Du- 
trochet  endosmose,  and  the  outward  flow  exosmose. 

The  upward  flow  of  sap  in  vegetables  is  due  to  a  similar  force  , 
the  ends  of  the  roots,  or  spongioles,  are  capillary  tubes,  and  they 
have  the  power  of  forcing  up  the  sap  to  the  leaves. 

The  force  of  these  capillary  tubes  is  not  confined  to  liquids,  but 
it  is  also  exerted  upon  gases.  If  a  piece  of  India  Fig.  is. 
rubber  be  tied  over  a  jar  of  carbonic  acid,  A,  Fig. 
13,  the  acid  will  force  its  way  out  so  much  faster 
than  the  air  rushes  in,  that  a  deep  concavity  will  33 
be  made  in  the  surface  of  the  rubber  ;  but  if  air 
be  placed  in  the  jar,  and  it  be  surrounded  by  an 
atmosphere  of  carbonic  acid,  the  rubber  will  be  forced  out  in  the 
form  of  a  ball,  B.  Gases  have  been  known  to  flow  through 
membranes  which  required  a  force  to  be  exerted  of  fifty  atmos- 
pheres, or  seven  hundred  and  fifty  pounds  to  the  square  inch. 

3.  Chemical  Affinity. — Another  kind  of  attraction  which  gov- 
erns matter  has  been  called  the  force  of  affinity,  or  chemical  af- 
finity. This  force  differs  from  cohesion  in  being  exerted  between 
atoms  of  different  kinds  of  matter,  and  in  being  attended  by  the 
formation  of  a  new  body  possessing  different  properties  from  either 
element  of  the  compound.  Cohesion  does  not  alter  the  properties 
of  the  atoms  which  it  causes  to  cohere  in  the  formation  of  a  mass. 

Those  changes  which  are  produced  by  chemical  force  or  affin- 
ity belong  to  the  subject  of  Chemistry,  and  are  not  the  specific 
objects  of  investigation  in  Natural  Philosophy.  They  pertain  to 
the  composition  of  bodies,  the  atoms  being  so  arranged  that  when 
they  are  separated  they  are  resolved  into  their  original  forms. 
Cohesion  may  act  between  atoms  of  the  same  kind  in  either  body 
before  they  are  combined  to  form  the  compound,  and  between  the 

What  is  endosmose  and  what  exosmose  ?  How  does  the  capillary  force 
act  upon  gases  ?  Difference  between  chemical  affinity  and  cohesion.  To 
what  science  do  those  changes  belong  which  are  produced  by  chemical  af- 
finity? 


ATTRACTION    OF    GRAVITATION.  35 

atoms  of  the  compound  after  it  is  formed,  but  has  nothing  to  do 
with  the  force  which  unites  them.* 

4.  Electrical   and   Magnetical    Attraction. —  The    polarity 
spoken  of  in  relation  to  the  atoms  of  matter,  in  the  formation  of 
crystals,  seems  to  pervade  masses  so  that  an  attractive  and  re- 
pulsive force  is  given  to  bodies  under  certain  conditions.     This 
state  of  polarity  is  sometimes  permanent,  as  in  the  case  of  mag- 
netism, and  at  others  it  only  exists  while  certain  conditions  are 
maintained,  as  in  the  case  of  electrified   bodies — that   arising 
from  common  and  Voltaic  electricity.     This  kind  of  attraction 
will  be  specially  considered  in  the  chapters  on  Electricity  and 
Magnetism. 

5.  Attraction  of  Gravitation,  or  Gravity,  is  generally  described 
as  that  property  by  which  bodies  tend  toward  the  center  of  the 
earth.     This,  however,  is  a  limited  view  of  the  case,  the  one 
which  is  confined  to  mechanical  philosophy.     This  property  exists 
among  masses  at  all  distances,  and  tends  to  bring  them  together. 

It  differs  from  cohesion  in  the  fact  that  it  not  only  exerts  its 
force  upon  atoms  which  are  near  each  other,  but  also  upon  those 
which  are  far  separated.  Its  force,  too,  does  not  depend  upon 
any  other  property,  but  is  universally  as  tJie  quantity  of  matter, 
and  must,  therefore,  be  connected  with  the  atoms  themselves. 
It  is  the  most  important  force  in  Natural  Philosophy,  giving  rise, 
in  common  with  inertia,  to  all  the  motions  of  the  heavenly  bodies, 
and  to  many  of  the  changes  which  take  place  on  the  surface  of  the 
earth.  It  is  important  to  examine  it,  therefore,  somewhat  in  detail. 

Attraction  of  Gravitation  is  witnessed  in  the  fact  that  two 
bodies  in  space  have  a  tendency  to  approach  each  other,  and,  if 
one  body  be  much  greater  than  the  other,  the  lighter  body  will 
have  a  perceptible  motion  ;  as,  when  a  stone  is  let  fall,  it  moves 
toward  the  center  of  the  earth ;  but  the  plumb-line  at  the  base 
of  a  mountain  will  not  obey  the  force  of  gravity  in  the  specific 
sense,  and  fall  toward  the  center  of  the  earth,  but  will  incline 
*  See  Gray's  Chemistry,  Chemical  Affinity,  for  a  full  view  of  this  force. 

Describe  the  other  kinds  of  attraction.  Gravitation,  &c.  How  does 
gravity  differ  from  cohesion  ?  With  what  is  this  force  connected  ?  How 
does  this  force  manifest  its  existence  ? 


36  NATURAL    PHILOSOPHY. 

toward  the  mountain,  as  was  proved  by  Dr.  Maskelyne,  in  his 
celebrated  experiments  near  the  Schehallien  Mountain,  in  Scot- 
land. It  has  been  supposed  that  logs  of  wood  in  a  pond  are 
drawn  together  by  this  force,  but  the  phenomenon  may  be  at- 
tributed to  capillary  attraction  (p.  33). 

It  is  due  to  the  general  attraction  of  one  body  for  another,  and 
of  each  part  for  every  other  part,  that  the  earth  and  all  the  heav- 
enly bodies  are  round.  The  same  force  that  makes  a  dew-drop 
is  concerned  in  the  rounding  of  the  spheres,  in  the  rising  of  the 
tides,  and  the  revolution  of  the  heavenly  bodies. 

Although  the  attraction  of  gravitation  exists  between  all  bodies, 
however  small  or  distant,  yet  its  force  varies  according  to  the 
three  following  laws,  which  are  generally  stated  thus  : 

(1.)  The  force  of  gravity  is  proportioned  to  the  quantity  of 
matter.  If  we  consider  this  force  to  be  exerted  in  the  matter  of 
our  globe,  it  will  be  seen  that  all. the  atoms  will  mutually  at- 
tract each  other,  and  that  the  combination  of  all  the  attractions 
will  result  in  causing  small  bodies  to  tend  toward  its  center. 
Hence  we  gain  the  idea  of  iveight,  which  is  the  measure  of  the 
force  of  gravity  near  the  earth's  surface  ;  and  as  that  force  is  as 
the  quantity  of  matter,  the  weight  of  bodies  is  taken  as  equiva- 
lent to  their  quantity  of  matter.^ 

It  follows,  from  this  law,  that  all  bodies,  whatever  their  quan- 
tity of  matter,  must  fall  with  the  same  velocity  to  the  earth;  for, 
if  one  body  contain  twice  the  quantity  of  matter  which  another 
does,  it  will  be  attracted  with  twice  the  force,  and,  of  course,  will 
move  with  the  same  velocity.  A  lead  ball  and  a  feather  will 

*  In  this  case,  however,  it  is  essential  to  have  some  standard,  or  some- 
thing to  compare  different  weights  with.  A  given  quantity  of  water  is 
taken  by  measure,  as  a  cubic  foot,  and  counterpoised  in  a  balance  by  a 
solid,  and  called  1000.  This  solid  1000  ounces  may  then  be  divided  into 
parts,  and  constitute  a  series  of  weights  by  which  to  determine  the  relative 
quantity  of  matter  in  different  bodies,  or  their  weights.  If  it  is  divided 
into  1000  parts,  of  course  each  part  will  be  an  ounce;  into  one  fourth  as 
many,  they  will  make  a  four  ounce  weight ;  into  one  sixteenth  as  many,  a 
pound  weight.  See  page  105. 

Why  are  the  heavenly  bodies  round  ?  How  does  the  force  of  gravity 
operate?  Illustrate  the  first  law  of  gravitation.  What  is  weight,  and 
how  is  a  standard  of  weight  formed  ?  Will  large  bodies  fall  with  greater 
or  less  velocity  than  small  ones  ? 


UKIVElfeSIT 


LAWS    OF    GRAVITATION. 

fall  to  the  earth  in  the  same  time  from  the 

is  not  the  fact  in  nature,  because  of  the  resistance 

mosphere  offers.     But, 

Fig.  14.      Exp. — If  a  guinea  and  a  feather,  a,  b,  Fig.  14,  be  placed  in  a 
/fT\     long  glass  tube,  and  the.  air  exhausted  from  the  tube,  both  will 
fall  from  one  end  to  the  other  in  the  same  time. 
) 

(2.)  The  second  law  is,  The  force  of  gravity  varies  in* 

versely  as  the  square  of  the  distance  from  the  center  of 
the  earth  ;  or  generally,  "  The  attraction  of  gravitation 
is  inversely  as  the  square  of  the  distance."  "  Inversely" 
means  "  that  as  the  distance  increases,  the  force  dimin- 
ishes." "  As  the  square  of  the  distance"  means  that,  if 
we  take  distances  represented  by  1,  2,  3,  4,  or  once,  twice, 
or  three  times  any  given  distance,  the  square  of  these 
numbers  will  make  the  series  1,  4,  9,  16.  The  radius  of 
the  earth,  4000  miles,  is  taken  as  unity.  A  body  weigh- 
ing one  pound  at  the  earth's  surface,  or  4000  miles  from  the 
earth's  center,  will  weigh  but  one  fourth  as  much  at  twice  the 
distance,  or  8000  miles  from  the  center ;  one  ninth  as  much  at 
three  times  the  distance,  or  12,000  miles ;  and  one  sixteenth  as 
much  at  four  times  the  distance,  or  16,000  miles  from  the  center 
of  the  earth.  This  law  may  be  illustrated  by  a  diagram,  as  it 
applies  to  all  forces  acting  from  a  center,  and  geometrically  de- 
monstrated. 

Let  C,  Fig.  15,  be  the  center  of  the  earth.     The  force  of 


Fig.  15. 


gravity  contained  in  the 
earth  may  be  conceiv- 
ed to  proceed  from  this 
center.  Now,  any  in- 

c  fluence  proceeding  in 
right  lines,  and  in  ev- 
ery direction,  from  the 
center  of  the  earth,  as 
light,  heat,  and  gravity, 
will  diminish  inversely 
as  the  square  of  the  dis- 

r  tance.    For,  let  the  dis- 


What  is  the  second  law  of  gravity  ?     What  is  meant  by  inversely,  square 
of  the  distance  1     How  may  this  law  be  proved  ? 


38  NATURAL    PHILOSOPHY. 

tance  CA  be  4000  miles,  and  CF  8000  miles  from  the  center,  C, 
the  surface  FGHI  will  be  four  times  the  surface  ABDE  ;  and, 
of  course,  as  the  force  is  spread  over  four  times  the  space,  it  will 
be  but  one  fourth  as  great  over  the  same  space  at  the  former  as  at 
the  latter  distance.  That  is,  the  space  ABDE  :  FGHI :  :  AB* 
:  FG2,  or  CA2 :  CF2  ;*  or  the  force  of  gravity  at  twice  the  distance 
from  its  source  is  spread  over  four  times  the  space,  and,  of  course, 
is  but  one  fourth  as  strong. 

As  we  descend  from  the  surface  of  the  earth  to  its  center,  a 
different  law  prevails  ;  for,  if  we  suppose  a  body  carried  from  the 
surface  to  the  center  of  the  earth,  the  force  toward  the  center 
would  be  constantly  diminished  by  the  attraction  of  the  quantity 
of  matter  which  the  body  left  behind  it. 

Thus,  suppose  A  B,  Fig.  16,  represents  the  earth,  C  the  cen- 
ter, and  d  a  body  2000  miles  from  the 
center.  It  can  be  proved  that  the  body,  d, 
would  remain  at  rest  in  any  part  of  a  hol- 
low sphere  of  uniform  density.  The  force, 
therefore,  which  attracts  it  toward  the  cen-  , 
ter  will  be  exerted  only  by  the  matter  in 
x  d  e,  the  exterior  portions  having  no  tend- 
ency to  attract  it  toward  the  center.  As 
the  force  of  attraction  is  proportioned  to 
the  quantities  of  matter,  the  matter  in  A  B  is  to  that  in  d  x  e  as 
A  C3  to  d  C3 ;  but  the  force  varies  inversely,  as  A  C2  and  d  C2 ; 
.-.  the  force  at  A  :  d  :  :  A  C3-^  A  C2 :  d  C3+d  C2,  or  : :  A  C  :  d  C. 

The  third  law  is,  that  the  force  of  gravity  from  the  center  to 
the  surface  of  the  earth  is  directly  as  the  distance  ;  the  greater 
the  distance,  the  greater  the  force,  and  the  less  the  distance,  the 
less  the  force.  A  body,  then,  falling  through  a  hole  made  through 
the  earth's  center,  if  the  air  were  removed,  would  fall  to  the  cen- 
ter, where  it  would  weigh  nothing  ;  but  another  force  would  be 
generated,  which  would  carry  it  to  the  opposite  side. 

One  pound  at  the  surface  would  weigh  half  a  pound  2000 

*  Two  similar  triangles,  CFG,  CAB,  are  to  each  other  as  the  squares  of 
their  homologous  sides  CA  and  CF,  or  AB,  FG ;  but  CF  is  double  CA,  and 
FG  double  AB  ;  but  the  square  on  half  a  line  is  one  fourth  the  square  upon 
the  whole  line. 

Does  the  force  of  gravity  increase  or  diminish  as  we  descend  toward  the 
center  of  the  earth?  Illustrate  this  law.  What  would  a  body  weigh  at 
the  center  of  the  earth  ? 


PROBLEMS.  39 

miles  from  the  center,  three  quarters  of  a  pound  3000  miles  from 
the  center,  a  quarter  of  a  pound  at  1000  miles,  and  in  the  same 
ratio  for  all  other  distances. 

PROBLEMS. 

In  order  to  render  the  above  laws  familiar,  the  following  prob- 
lems are  added  : 

1.  What  would  be  the  weight  of  a  sixty-four  pound  cannon 
ball  at  the  distance  of  the  moon,  240,000  miles  ? 

Ans.,  ¥f  j  libs. 

2.  A  meteoric  stone  was  observed  4000  miles  from  the  earth, 
to  which  it  fell,  and  was  found  to  weigh  2000  Ibs.     What  would 
it  have  weighed  at  the  point  where  it  was  first  observed  ? 

Ans.,  500  Ibs. 

3.  What  would  a  ton  of  iron  weigh  500  miles  from  the  sur- 
face of  the  earth  ?* 

Ans.,  158011-  Ibs. 

4.  What  would  a  ton  of  iron  weigh  500  miles  below  the  sur- 
face of  the  earth  ?.    What  500  miles  from  its  center  ? 

Ans.,  1750  Ibs.,  and  250  Ibs. 

If  the  formula  in  the  note  below  be  applied  to  the  third  ex- 
ample in  numbers,  the  loss  of  weight  will  be  equal  to 

2000(2X4000X500+250,000)      __8,500,000,000_       6J 
16,000,000-j-2  X  4000  X  500-j-25,000~~  20,250,000    ~ 

If  the  height  is  not  more  than  half  a  mile,  x*  may  be  neglect- 
ed,  and  then  the  formula  will  be  W—  W7= 


*  Let  A,  Pig.  17,  be  the  earth,  C  its  center,  x  the 
height  from  the  surface,  then  will  the  weight  at  s  be 
to  the  weight  at  x  as  the  squares  of  the  distances  Cx 
and  Cs.  Now,  to  find  the  loss  of  weight,  we  must  sub- 
tract the  weight  at  x  from  the  weight  at  s,  and  then, 
if  we  represent  the  weight  at  s  by  W,  and  at  x  by  W  ; 
also,  Cs  by  r,  and  sx  by  x,  we  shall  have  the  proportion 


W  :  W—  W  :  :  (r+x?  :  2rx+x*,  or  W  :  W  —  W  :  :  r*+2rx+x*  :  2r*-f-a;2, 
The  loss  of  weight,  then,  will  be  =  W  —  w/= 


What  is  meant  by  inertia  ? 


40  NATURAL    PHILOSOPHY. 

II.  Inertia,  as  well  as  gravity,  or  attraction  in  general,  and  re- 
pulsion, is  sometimes  called  a  property  of  matter,  but  it  is  one  of 
the  principal  forces  which  govern  matter. 

Inertia  is  a  peculiar  force ;  it  is  the  force  of  resistance  to  a 
change  of  state.  Thus,  when  a  body  is  at  rest,  it  requires  some 
force  to  put  it  in  motion.  This  resistance,  or  inertia  of  a  body, 
is  proportioned  to  the  quantity  of  matter.  So,  also,  when  any 
body  is  in  motion,  as  a  carriage  or  rail-road  car,  it  acquires  a 
force  which  must  be  overcome  before  its  motion  can  be  stopped. 
But  the  force  in  this  case  will  vary  with  the  velocity  of  the  mov- 
ing body,  and  is  not  a  measure  of  the  quantity  of  matter. 

This  force  of  inertia  is  exemplified  in  the  most  common  phe- 
nomena in  life,  in  walking,  riding,  and  in  all  cases  where  mo- 
tion is  generated  or  destroyed.  It  is  used  to  regulate  the  motion 
of  machinery,  as  in  the  fly-ivheel. 

This  force  is  so  important  that  it  will  be  more  fully  illustrated 
in  connection  with  Motion  and  its  laws. 

There  are  other  forces,  such  as  the  muscular  force,  the  force 
of  gunpowder,  &c.,  but  we  have  given  a  general  view  of  such  as 
belong  to  matter  as  such. 

Matter  in  the  mass,  then,  consists  of  minute  atoms,  which  are 
endowed  with  extension  and  impenetrability.  It  is  governed  by 
the  forces  cohesion  and  repulsion,  which  give  rise  to  the  forms 
solid,  liquid,  and  gas,  and  to  properties,  as  density,  hardness,  elas- 
ticity, tenacity,  &c.  It  is  also  governed  by  capillary  attraction, 
chemical  affinity,  electrical  attraction,  magnetic  attraction,  the 
attraction  of  gravitation,  and  the  force  of  inertia. 

We  now  proceed  to  note  the  effects  of  these  forces  and  the 
laws  of  their  action,  or  the  doctrine  of  Motions  and  Forces. 

How  is  inertia  estimated  when  bodies  are  at  rest?  How  when  they 
are  in  motion  ?  What  other  forces  exist  ?  Repeat  those  which  have  been 
named,  and  the  properties  which  result  from  them. 


MOTION    AND    ITS    LAWS.  41 


CHAPTER  II. 

MOTION  AND  ITS  LAWS.— INERTIA. 
SECTION  I.— OF  MOTION. 

Motion  is  a  change  of  place.     It  is  of  several  kinds  : 

1st.  Absolute;  that  is,  motion  in  reference  to  a  fixed  point. 

2d.  Relative ;  that  is,  the  motion  of  one  body  in  respect  to 
another  in  motion. 

3d.  Apparent ;  tliat  is,  ivhen  bodies  appear  to  move  in  cons&> 
quence  of  the  motions  of  other  bodies. 

4th.  Real;  that  is,  ivhen  a  body  is  in  actual  motion •:  a  con- 
dition which,  taking  the  whole  universe  into  view,  pertains  to 
all  matter. 

MOTION  is  the  change  of  place  among  bodies.  It  is  divided 
into  absolute  and  relative,  apparent  and  real. 

1 .  Absolute  Motion  refers  to  a  change  of  place  in  reference  to 
some  point  that  is  fixed.     Thus,  when  a  man  walks  from  his 
house  to  the  church,  he  has  an  absolute  motion  as  regards  both 
his  house  and  the  church. 

2.  Relative  Motion  has  reference  to  a  change  of  place  between 
two  or  more  bodies  which  are  in  motion.     Thus,  a  man  walking 
on  the  deck  of  a  sailing  ship  has  a  motion  with  the  ship  and  in 
respect  to  the  ship.     If  he  walk  toward  the  stern  as  fast  as  the 
ship  sails,  he  has  a  relative  motion  in  respect  to  the  ship,  and  ab- 
solute rest  in  respect  to  the  earth.     So  two  men  traveling  with 
different  velocities-  have  a  motion  relative  with  regard  to  them- 
selves, but  absolute  in  reference  to  the  point  from  which  they 
started  or  to  which  they  tend,  but  not  in  respect  to  the  earth  it- 
self; for  the  earth  has  two  motions,  one  from  west  to  east,  and 
one  in  its  orbit  around  the  sun,  and  all  bodies  on  its  surface  par- 
take of  these  two  motions.     Hence  every  body  on  the  earth's 

Define  motion.     What  is  absolute  and  what  relative  motion  2 


42  NATURAL   PHILOSOPHY. 

surface  is  either  in  relative  motion  or  relative  rest  as  it  respects 
the  earth  itself. 

Now  the  earth  revolves  in  its  orbit  about  100,000  feet  per 
second.  The  velocity  of  a  cannon  ball  is  not  greater  than  2000 
feet  per  second.  If,  then,  it  be  fired  in  the  direction  in  which 
the  earth  moves,  its  motion  will  only  be  increased  to  102,000 
feet  per  second ;  if  fired  in  the  opposite  direction,  its  motion  will 
be  decreased  to  98,000  feet  per  second.  But  the  earth  moves 
from  west  to  east  about  1500  feet  per  second.  A  ball  fired  at 
that  rate  toward  the  west  would  be  relatively  at  rest  in  respect 
to  a  fixed  star,  its  motion  toward  the  west  being  just  counteracted 
by  the  earth's  motion.  In  fact,  the  cannon  would  move  away 
from  the  ball ;  it  would  be  in  a  state  of  absolute  motion  and  rel- 
ative rest.  Now  it  has  been  shown  that  all  the  heavenly  bodies 
are  in  motion,  so  that  absolute  rest,  when  we  look  at  the  universe 
as  a  whole,  is  not  a  condition  of  matter. 

It  appears  highly  probable,  for  several  reasons,  that  the  atoms 
of  matter  are  in  a  constant  state  of  vibration ;  due,  perhaps,  to 
the  relative  intensity  of  attraction  and  repulsion  which  exist 
among  them,  and  which  are  constantly  varying  as  the  tempera- 
ture of  bodies  varies. 

3.  Apparent  Motion.- — When  the  seeming  motion  of  a  body 
actually  at  rest  arises  from  the  real  motion  of  a  body  apparently 
at  rest,  it  is  called  apparent.     This  apparent  motion  generally 
arises  from  the  apparent  rest  of  the  observer.     Thus,  in  riding  in 
a  rail-road  car,  by  not  becoming  conscious  of  our  own  motion,  all 
the  external,  visible  world,  houses,  trees,  fences,  &c.,  appear  to 
be  hurrying  past  with  great  velocity. 

The  revolution  of  the  heavenly  bodies  apparently  from  east 
to  west  is  due  to  the  actual  motion  of  the  earth  on  its  axis  in 
an  opposite  direction. 

4.  Real  Motion. — As  all  the  heavenly  bodies  are  in  motion,  it 
is  difficult   to    determine  what  bodies  are  in  actual  or  real  mo- 
tion, and  what  in  apparent.     If  we  know  any  cause  which  should 

How  rapidly  does  the  earth  move  in  its  orbit?  How  fast  from  west  to 
east  1  Velocity  of  a  cannon  ball  ?  Are  there  any  bodies  in  a  state  of  abso- 
lute rest?  Apparent  and  real  motion  defined.  How  can  we  determine 
real,  and  how  apparent  motion  ? 


LAWS    OF    MOTION.  43 

give  motion  to  one  body  and  not  to  another,  or  if  the  tendency 
of  their  motion  is  in  one  uniform  direction,  we  may  regard  it  as 
real,  and  not  apparent.  . 


SECTION  II.— LAWS   OF  MOTION  IN  THEIR  RELATION  TO  FORCES,  ESPE- 

CIALLY  TO  THE  FORCE  OF  INERTIA. 

• 

In  consequence  of  the  inertia  of  matter,  force  is  necessary  to 
produce,  to  destroy,  or  to  cfiange  the  motion  of  a  body. 

Motion  is  as  natural  to  bodies  as  rest ;  hence  the  first  laiv  of 
Motion  is,  that  a  body  will  continue  in  tlue  state  in  which  it  is, 
either  of  rest  or  of  uniform,  rectilinear  motion,  unless  acted  on 
by  some  force  to  change  its  condition :  a  law  which  is  also 
proved  by  experiment  and  observation. 

A  state  of  motion  is  therefore  as  permanent  as  a  state  of  rest  ; 
though,  in  consequence  of  the  resistance  of  the  air  and  the  attrac- 
tion of  gravitation,  bodies  in  motion  near  the  earth  are  soon 
brought  to  a  state  of  rest ;  but  the  heavenly  bodies  are  in  a  state 
of  perpetual  motion. 

Motion  is  naturally  uniform  ;  that  is,  bodies  move  over  equal 
spaces  in  equal  times. 

In  consequence,  also,  of  the  inertia  of  matter,  motion  is  al- 
ways in  proportion  to,  and  in  the  direction  of  the  force  impress- 
ed, ivhich  is  the 

Second  law  of  Motion  ;  and,  for  a  similar  reason*; 

Action  and  reaction  are  equal,  and  in  opposite  directions, 
^vhich  is  the 

Third  law  of  Motion. 

Force  is  that  which  moves,  tends  to  move,  or  to  counteract  the 
motion  of  a  body.  All  forces  we  have  already  noticed  may  be 
reduced  to  four,  attraction,  repulsion,  inertia,  and  muscular  force. 

Every  motion  is  the  result  of  some  active  force,  and  yet  a 
state  of  rest  is  no  more  natural  to  bodies  than  a  state  of  motion. 
A  body  at  rest  requires  force  to  put  it  in  motion  by  overcoming 
its  inertia.  A  body  in  motion  requires  force  to  stop  it,  or  to  over- 
come its  inertia.  Hence 

Define  force.    What  is  the  natural  state  of  bodies  ? 


44  NATURAL    PHILOSOPHY. 

Tlie  First  Law  of  motion  is,  that  a .  body  continues  in  the 
state  in  which  it  is,  either  of  rest  or  uniform  rectilinear  motion, 
unless  acted  on  by  some  force  to  change  its  condition. 

1.  That  a  body  at  rest  requires  force  to  put  it  in  motion,  results 
directly,  as  we  have  seen,  from  its  inertia,  which  must  be  over- 
come in  order  that  the  motion  may  take  place.  The  attraction 
of  the  earth,  for  example,  is  just  sufficient  to  cause  a  body  to  fall 
toward  it  sixteen  and  one  twelfth  feet  in  a  second ;  but  if  there 
were  no  inertia  to  be  overcome,  it  would  fall  with  the  speed  of 
lightning,  in  which  case  it  would  exert  no  force  as  it  fell. 

This  law  is  proved  by  universal  experience,  but  it  may  be  il- 
lustrated by  numerous  experiments  and  examples,  and  by  refer- 
ence to  the  most  familiar  natural  phenomena.  Thus  we  know, 
that,  in  order  to  impart  motion  to  any  body  at  rest,  we  must  al- 
ways employ  force  of  some  kind,  and  a  force  proportioned  to  the 
weight  of  the  body. 

The  inertia  of  a  body  at  rest,  however,  is  not  overcome  at  once, 
but  time  is  required  for  the  force  to  be  impressed  upon  it. 

We  have  observed,  for  instance,  that  when  a  large  load  is  to 
be  moved,  as  a  loaded  train  of  cars  by  a  single  locomotive,  all  of 
them  could  not  be  set  in  motion  at  the  same  instant.  Greater 
effort  is  required  to  set  a  carriage  in  motion  than  to  keep  it  in 
motion,  because  its  inertia  mustjirst  be  overcome. 

This  fact  is  beautifully  illustrated  by  an  apparatus  called  the 
Inertia  Apparatus,. 

Exp. — In  Fig.  18  a  marble  ball,  a,  is  placed  upon  a  card,  c,  and  a  spring, 
d,  is  forced  against  the  card.  The  card  is  thrown  j^..  is. 

out   from  under  the  ball,  leaving  it  upon  the 
stand. 

Exp. — The  same  may  be  shown  by  laying  a 
dollar  on  a  card,  balanced  upon  the  tip  of  the  fin- 
ger. By  snapping  the  finger  suddenly  against 
the  edge  of  the  card,  the  card  will  be  forced  out, 
leaving  the  dollar  balanced  on  the  finger  in  place 
of  the  card. 

So,  by  a  sudden  blow,  a  piece  may  be  broken  off  from  any 

First  law  of  motion.  How  is  this  law  proved  ?  How  much  time  is  re- 
quired to  overcoma  the  inertia  of  matter?  Illustration.  Inertia  appara- 
tus. Desci'ibe  the  experiments  to  illustrate  the  inertia  of  matter.  Why 
will  a  sudden  blow  break  off  a  piece  from  a  solid  ? 


FIRST    LAW^OF   MOTION.  45 

solid  "body  without  injury  to  the  adjoining  parts.  A  "ball  may 
be  fired  through  a  pane  of  glass,  making  only  an  aperture  where 
it  strikes  it ;  or  a  soft  body,  as  a  tallow  candle,  may  be  fired 
through  a  board,  because  in  each  case  there  is  not  time  for  the 
force  to  be  distributed  over  the  parts,  and,  being  concentered  upon 
the  points  struck,  the  cohesion  in  those  parts  suddenly  gives  way. 
Glass  vessels  are  often  broken  by  taking  them  up  hastily  by  the 
handle. 

When  a  horse  suddenly  starts  with  a  load,  there  is  danger  of 
his  breaking  some  part  of  his  harness.  If  one  stands  in  a  wagon 
when  it  is  suddenly  pulled  forward,  there  is  danger  of  having  his 
feet  pulled  out  from  under  him,  and  his  body  thrown  in  an  oppo- 
site direction.  If  we  wish  to  raise  a  heavy  weight  with  a  slen- 
der rope,  the  strain  should  be  gradual,  lest  a  sudden  pull  should 
break  it. 

In  these  and  numberless  other  instances,  which  the  student  may 
easily  supply,  there  are  both  proof  and  illustration  of  the  resistance 
of  inertia,  and  of  the  necessity  of  overcoming  it  to  produce  mo- 
tion ;  and,  in  general,  force  should  be  applied  gradually,  some 
time  being  required  to  impart  motion  to  the  whole  mass. 

2.  Force,  on  the  other  hand,  is  equally  requisite  to  stop  a  body 
in  motion  ;  or,  a  body  in  motimi  has  a  tendency  to  continue  in 
motion.  This  also  results  directly  from  inertia,  for  there  is  no 
power  in  the  body  to  change  its  state,  and  hence  some  external 
force  must  be  applied.  Illustrations  of  this  property  of  motion 
are  equally  numerous  with  the  preceding. 

It  is  proved  by  observation  that  if  the  propelling  force  of  one 
or  more  bodies  in  motion  is  removed,  they  will  continue  to  move 
forward  by  the  force  of  their  inertia.  Thus,  when  the  engine  is 
detached  from  a  train  of  cars,  they  move  forward  with  great 
velocity  by  the  force  of  their  inertia ;  so,  when  a  horse  suddenly 
stops,  he  throws  his  rider  over  his  head.  When  a  wagon  in 
motion  strikes  against  any  solid  body,  the  driver  is  thrown  for- 
ward. A  case  in  court  was  once  decided  by  the  testimony  of 

What  illustrations  of  the  resistance  of  matter  to  motion  ?  What  is  neces- 
sary to  stop  the  motion  of  any  body  ?  Why  will  a  train  of  cars  continue 
to  move  after  the  engine  is  detached  1 

• 


46  NATURAL   PHILOSOPHY. 

the  plaintiff's  witness,  that  the  shock  was  so  great  that  he  was 
thrown  to  a  great  distance.  This  fact  showed  that  his  own 
vehicle  was  in  rapid  motion,  not  that  of  the  defendant.  Were 
the  motion  of  the  earth  suddenly  stopped,  we  should  be  launch- 
ed into  space  with  the  velocity  with  which  the  earth  is  moving, 
about  100,000  feet  per  second  ;  a  velocity  more  than  fifty 
times  greater  than  a  cannon  ball. 

Arnott  gives  an  account  of  an  African  traveler  who  saw  him- 
self pursued  by  a  tiger,  from  which  he  could  not  escape  by  run- 
ning, but  perceiving  that  the  animal  was  watching  an  opportu- 
nity to  seize  him  by  its  usual  spring  or  leap,  he  artfully  led  it  to 
where  the  plain  was  terminated  by  a  precipice  hidden  by  brush- 
wood, and  he  had  but  just  time  to  transfer  his  hat  and  coat  to  a 
bush,  and  to  retreat  a  few  paces,  when  the  tiget  sprang  upon  the 
bush,  and,  by  the  motal  inertia  of  his  body,  was  carried  over  the 
precipice  and  destroyed. 

The  destructive  effect  of  bomb  shells  is  due  to  the  same  prin- 
ciple. When  they  burst,  the  various  materials,  balls,  &c.,  with- 
in them  partake  of  the  same  velocity  as  the  whole  shell,  and  scat- 
ter death  and  destruction  around.  The  good  effects  of  riding,  as 
an  exercise,  are  due  to  the  inertia  of  the  blood  in  the  veins. 
When  the  body  moves  up  and  down,  the  blood,  by  its  inertia,  is 
also  set  in  motion  in  an  opposite  direction. 

Motion,  in  consequence  of  the  force  of  inertia  which  it  gen- 
erates, is  as  permanent  a  state  of  matter  as  rest,  and  yet  there'  is 
a  general  opinion  that  any  body  in  motion  will  naturally  come 
to  a  state  of  rest.  We  often  observe  bodies  in  motion*  and  also 
notice  that  they  all,  on  the  surface  of  the  earth,  gradually  be- 
come quiescent.  But  this  is  due  to  friction,  gravity,  and  the  re- 
sistance of  the  air.  If  these  forces  were  removed,  a  body  once 
set  in  motion  would  never  stop. 

(1.)  Influence  of  Friction. — Thus  we  may  easily  show  the  in- 
fluence of  friction  upon  a  body.  If  a  ball  be  rolled  over  a  rough 
surface,  it  is  soon  brought  to  a  quiescent  state  by  friction.  If  it 

What  would  be  the  effect  of  stopping  the  earth  in  its  orbit  1  What  oth- 
er illustrations  of  inertia  1  Why  does  the  motion  of  bodies  near  the  earth 
cease  ?  What  is  the  influence  of  friction,  gravity,  and  the  resistance  of  the  air  ? 


UNIFORM    MOTION.  47 

be  rolled  on  a  smooth  plane,  it  will  continue  in  motion  much 
longer. 

(2.)  Gravity. — If  there  were  no  friction  of  the  surface,  the  force 
of  gravity  drawing  it  continually  toward  the  center  of  the  earth 
would  finally  bring  it  to  a  state  of  rest,  unless  its  velocity  were 
sufficient  to  overcome  gravity,  which  would  require  a  rate  nine- 
teen times  more  rapid  than  at  present.  In  this  case  it  would 
continue  to  revolve  about  the  earth,  and  its  motion  would  be  per- 
petual. 

(3.)  Resistance  of  the  Air. — The  resistance  of  the  air  is  also 
considerable,  which  aids  in  bringing  all  bodies  projected  through 
it  to  a  state  of  rest ;  but  if  this  resistance  is  removed,  the  motion 
will  be  much  longer  continued.  Thus  a  top  in  an  exhausted  re- 
ceiver will  revolve  for  hours.  A  pendulum  in  the  same  condi- 
tion has  been  known  to  vibrate  for  a  day. 

Exp. — But  a  beautiful  illustration  of  the  resistance  of  the  air  as  influ 
Fi    ig  encing  motion  is  shown  in  two  fan-wheels,  Fig 

19.  When  set  in  motion  in  the  air,  one  of  them,  b, 
is  soon  brought  to  rest  because  of  the  greater  re- 
sistance it  meets  with.  But  if  they  are  both  re- 
volved in  the  exhausted  receiver  of  an  air  pump, 
they  will  both  continue  in  motion  for  the  same 
length  of  time. 

Now,  as  we  remove  opposing  forces,  we 
observe  that  the  motions  of  bodies  are  long- 
er continued,  and  hence,  if  all  such  forces 
were  removed,  motion  would  become  as  per- 
manent as  rest.  In  fact,  when  we  observe 
the  motions  of  the  heavenly  bodies,  we  find 
their  course  is  perpetual.  The  revolution  of  the  planets  around 
the  sun  is  accomplished  by  two  forces.  One  is  the  force  of  in- 
ertia, by  which  they  always  tend  to  move  in  a  straight  line,  and 
the  other  the  attraction  of  gravitation,  which  causes  them  all  to 
move  toward  the  sun.  A  planet  once  set  in  motion  with  a  force 
sufficient  to  carry  it  around  the  sun,  will  never  lose  that  motion, 
but  continue  to  move  on  forever.  t 

3.  Motion  is  naturally  uniform. — If  force  is  required  alike 

Where  shall  we  find  the  best  illustrations  of  this  law  1  What  is  meant 
by  uniform  motion  ? 


48 


NATURAL    PHILOSOPHY. 


Fig.  20. 


to  move  or  to  stop  a  body  in  motion,  it  follows  that  the  body 
will  move  over 

Equal  spaces  in  equal  times,;  that  is,  undisturbed  motion  is 
uniform.  This  is  proved  by  the  revolutions  of  all  the  heavenly 
bodies,  the  great  standard  of  uniform  motion  being  the  diurnal 
and  annual  revolutions  of  the  earth.  With  such  uniform  cer- 
tainty do  all  the  heavenly  bodies  revolve,  that  any  phenomenon, 
as  an  eclipse^  may  bev  calculated  thousands  of -years  before  its  oc- 
currence. We  rarely  «ee,  to  be  sure,  uniform  motion  upon  the 
surface  of  the  earth,  owing  to  the  presence  of  the  same  causes 
which  bring  all  bodies  to  a  state  of  rest,  but  we  see  a  constant 
tendency  to  uniform  as  well  as  to  perpetual  motion.  Thus,  in 
falling  bodies,  there  is  the  resistance  of  the  air,  which  may  be  re- 
garded as  of  equal  effect  upon  the  body  for 
the  space  of  a  few  hundred  feet,  but  the  force 
of  gravity  is  exerted  at  successive  instants, 
and  a  body  falls  with  a  velocity  which  is  said 
to  bq  uniformly  accelerated.  Now  if  'the 
force  of  gravity  could  be  counteracted  after 
the  body  had  received  the  first  impulse,  it 
would  fall  over  equal  spaces  in  equal  success- 
ive portions  of  time. 

'Atwoods  Machine. — The  force  of  gravity 
is  just  balanced  in  an  apparatus  for  falling 
bodies,  called  Atwoods  Machine.  Fig.  20 
contains  all^the  parts  essential  to  its  opera- 
tion. By  counterpoising  two  weights,  m  n, 
attached  by  a  string  and  passing  over  a  fric- 
tion wheel,  the  force  of  gravity  is  overcome, 
and  by  adding  a  slight  force  to  impart  motion 
to  one  of  the  weights,  n,  it  is  found  by  experi- 
ment that  it  will  move  over  equal  spaces  in 
equal  times,  or  with  a  uniform  'motion. 

4.  Motion  is  naturally  rectilinear.- — If 
force  is  required  to  move  a  body  or  to  stop  its 
^notion,  it  will  require  force  to  bend  it  from 

Examples  ef  uniform  motion.  Describe  Atwood's  Machine.  How  does 
it  prove  that  motion  is  naturally  uniform  ?  How  is  the  tendency  to  rec- 
tilinear motion  proved  1 


SECOND   LAW    OF    MOTION. 


49 


a  rectilinear  direction.  Under  the  influence  of  its  inertia,  mat- 
ter has  a  tendency,  as  we  have  seen,  to  move  uniformly ;  it  has 
also  a  tendency  to  move  in  right  lines,  though  this  disposition 
is  rarely  carried  out  in  nature,  nearly  every  motion  being  either 
circular  or  curvilinear.  All  the  heavenly  bodies  move  in  curves  ; 
bodies  on  the  surface  of  the  earth  have  a  curvilinear  motion,  but 
the  tendency  to  move  in  right  lines  is  always  manifest.  It  is 
proved  by  the  fact  that  any  body  moving  around  a  center  will  fly 
off  in  the  direction  of  a  tangent  to  the  curve  in  which  it  is  mov- 
ing, as  water  from  a  grindstone  or  a  stone  from  a  sling,  if  the  force 
which  binds  it  to  the  center  is  destroyed.  This  tendency  to  break 
away  from  the  central  power  is  called  the  centrifugal  force,  and 
is  another  name  for  inertia,  while  the  force  which  confines  it  to 
the  center  is  termed  the  centripetal  force. 

The  tendency  of  bodies  to  move  in  straight  lines  is  beautifully 
illustrated  by  the  following  apparatus, 
Qmni ,.,  7   Fig.  21 :  two  balls  are  placed  on  a  bar, 
a  b,  which  may  be  made  to  revolve  rap- 
idly on  an  axis  ;  through  the  center  of 
3  this  axis  a  cord  passes,  one  end  attach- 
ed to  the  spring  c,  and  the  other  to  the 
balls.   When  the  axis  and  balls  are  turn- 
ed, the  balls  tend  to  pass  to  a  or  b,  and 
M-     — ^    i        consequently  bend  the  spring,  which  in- 
7»  H  VI       dicates  the  amount  of  centrifugal  force. 

3 1 — — '     1       If  the  balls  are  placed  near  the  axis  and 
J  u      are  free  to  move,  they  will  pass  to  a  and 

b  as  soon  as  the  revolution  has  generated  sufficient  centrifugal 
force  to  overcome  their  inertia. 

Second  Law. — Motion  is  proportioned  to  the  force  impressed, 
and  is  in  the  direction  in  which  the  force  acts. 

1 .  That  motion  is  in  proportion  to  the  force  impressed  upon  a 
body  is  proved  by  experiments  with  Atwood's  Machine.  Thus, 
by  means  of  different  weights,  c,  applied  to  n,  Fig.  20,  at  e,  and 
taken  off  by  the  brass  ring,  a,  different  velocities  may  be  given 
to  the  ball,  n.  It  is  found  that  the  velocity  of  n  in  a  given  time 

Describe  the  figure.  What  is  the  second  law  of  motion  ?  How  is  it 
proved  ? 

C 


50  NATURAL    PHILOSOPHY. 

will  increase  with  the  increase  of  force,  and  diminish  with  the 
diminution  of  force.  Twice  the  force  will  double  three  times  the 
force  with  treble  the  velocity. 

A  body  which  falls  two  seconds  has  twice  the  velocity  it  would 
have  by  falling  one,  and  the  impelling  force  is  just  twice  as 
great. 

This  constant  relation  between  the  force  and  the  velocity  of 
motion  is  a  matter  of  common  observation.  If  a  powerful  force 
be  used  upon  a  small  quantity  of  matter,  the  velocity  becomes 
very  great.  If  a  slight  force  be  used  upon  a  large  quantity  of 
matter,  the  velocity  will  be  proportionably  less.  Hence  any  force, 
however  small,  will  cause  motion  in  any  mass,  however  great. 
The  fall  of  an  apple  or  of  a  meteoric  stone  lifts  the  earth.  This 
may  seem  an  extravagant  assertion,  but  the  velocity  of  any  two 
bodies  toward  each  other  will  be  proportioned  inversely  to  their 
quantities  of  matter ;  for  it  is  the  matter  which  originates  the 
force,  and  hence  the  larger  body  will  move  as  much  slower  than 
the  smaller  as  its  quantity  of  matter  exceeds  it. 

The  quantity  of  motion,  then,  which  any  body  may  have,  is 
measured  by  the  velocity  and  quantity  of  matter.  Hence  the 
quantity  of  motion  in  any  body  is  an  exact  measure  of  the  force 
which  gave  rise  to  it ;  for  if  the  mass  is  great,  with  a  small  force 
its  motion  will  be  slow,  and  if  the  mass  is  small,  the  motion  will 
be  more  rapid,  but  in  each  case  the  quantity  of  motion  just  equals 
the  quantity  of  matter  multiplied  into  the  velocity.  The  quan- 
tity of  motion  is  also  called  momentum. 

In  consequence  of  the  inertia  of  a  body,  it  receives  a  given  force 
which  it  can  not  ose  except  by  imparting  it  to  other  bodies,  and 
hence  the  quantit  /  of  motion  or  momentum  of  any  body  is  the 
force  which  it  can  reproduce.  The  momentum  of  a  cannon  ball 
may  only  be  sufficient  to  destroy  a  single  man,  and  it  may  be 
able  to  pierce  through  the  walls  of  a  fort ;  it  may  set  a  body  in 
rapid  motion,  and  it  may  be  entirely  stopped  by  it.  In  each  case, 
the  force  it  generates  is  a  measure  of  the  force  by  which  it  was 

What  relation  has  force  to  velocity  ?  What  effect  has  the  fall  of  an  ap- 
ple upon  the  earth  ?  What  is  meaut  by  the  quantity  qf  motion  1  What  is 
momentum? 


THIRD    LAW    OF    MOTION.  51 

originally  impelled.  For  these  and  other  reasons,  it  is  clearly 
proved  that  force  and  motion  are  always  proportioned  to  each 
other. 

2.  Motion  is  always  in  the  direction  ofthefo^ce.  This  would 
also  seem  to  be  a  direct  inference  from  the  doctrine  of  inertia. 
If  the  inertia  of  a  body  is  overcome  by  any  force,  it  must  move 
in  the  direction  in  which  the  force  acts,  because  there  can  be  no 
reason  for  it  to  move  in  any  other  direction.  This  view  is  con 
firmed  by  experience.  We  should  be  astonished  to  find  a  ball 
which  was  acted  upon  by  a  force  toward  the  east  taking  a  con- 
trary direction,  or  at  all  deviating  from  the  course  we  designed 
it  to  take. 

Third  Law. — When  one  body  acts  upon  another,  action  and 
reaction  are  equal  and  in  opposite  directions. 

By  this  law  it  is  meant,  that  when  two  bodies  meet,  each 
gives  and  receives  exactly  the  same  shock. 

1.  This  law  may  be  easily  established  by  the  action  of  two 
Fig.  22.  balls,  a  b,  of  lead  or  clay,  suspended,  as 

in  Fig.  22,  by  small  cords,  so  as  to  move 
freely  through  the  arc  x  y.  The  balls 
are  of  exactly  equal  weight. 

(1.)  If,  therefore,  the  ball  a  fall  upon 
b  with  a  velocity  represented  by  6  0, 
both  balls  will  move  on  with  one  half 
the  velocity  of  the  first.  The  ball  a 
acts  on  b,  and  b  reacts  with  the  same 
force  on  a,  so  that  action  and  reaction 
are  equal. 

(2.)  If  b  is  larger  than  a,  then  the  momentum  of  the  two  after 
impact  will  be  just  equal  to  that  of  a  before ;  and,  generally, 
whatever  be  the  relation  of  a  to  b,  one  will  lose  just  as  much 
motion  as  the  other  acquires. 

(3  )  If  they  fall  with  equal  velocities,  but  in  opposite  directions, 
they  will  be  brought  to  rest,  which  shows  that  action  and  reac- 
tion are  not  only  equal,  but  in  opposite  directions. 

This  same  law  applies  to  bodies  at  rest.  If  one  body  press  upon 
another,  and  is  sustained  by  it,  the  second  body  must  react  with 

What  is  the  third  law  of  motion,  and  how  is  it  illustrated  and  proved  ? 
How  does  this  third  law  apply  to  bodies  at  rest  ? 


52  NATURAL    PHILOSOPHY. 

an  equal  force,  or  there  will  be  motion  of  both  bodies  ;  and  when- 
ever motion  takes  place,  it  is  due  to  the  same  cause  as  the  im- 
pact of  one  body  upon  another. 

2.  Numerous  illustrations  of  this  law  might  be  mentioned. 
The  following  are  a  few  of  them  : 

(1.)  Birds  fly  by  striking  the  air  with  their  wings.  If  the  ac- 
tion of  their  wings  against  the  air  was  not  met  by  an  equal  re- 
action, it  would  be  impossible  for  them  to  commence  their  flight, 
for  they  could  riot  raise  their  bodies.  By  striking  the  air  with  a 
force  sufficient  to  overcome  the  resistance  of  the  weight  of  their 
bodies,  they  are  borne  aloft.  If  the  wing  is  small,  it  must  move 
with  greater  velocity. 

(2.)  A  boat  is  forced  along  by  the  oar,  which  strikes  against 
the  water,  and  receives  from  the  water  an  equal  reaction. 

(3.)  When  two  men  meet,  the  shock  they  sustain  is  precisely 
equal,  and  it  makes  no  difference  whether  one  or  both  are  in 
motion.  The  one  standing  still  receives  and  imparts  the  same 
shock  as  the  one  who  is  in  motion ;  but  if  both  are  in  motion  at 
the  same  rate,  the  shock  is  twice  as  great. 

(4.)  Two  ships,  whether  both  are  in  motion  or  only  one,  strike 
each  other  with  equal  force,  and  when  both  are  in  motion  with 
great  velocity,  the  shock  becomes  very  great. 

(5.)  A  man  pulling  a  boat  by  a  rope,  or  two  bodies  attracted 
by  any  force,  exemplify  the  same  law.  Two  magnets  attract 
each  other  mutually  ;  the  influence  exerted  upon  one  is  given  back 
upon  the  other  ;  so  that,  if  several  forces  act  upon  each  other, 
they  have  not  the  power  of  changing  their  motion  in  the  slightest 
degree.  Thus,  if  twenty  men  in  a  boat  attempt  to  push  it  in  the 
same  or  in  opposite  directions,  they  may  exert  great  force,  but 
they  can  not  alter  the  direction  of  the  boat,  because,  if  they  all 
push  it  in  the  same  direction,  that  very  force,  by  reaction,  tends 
to  drive  it  equally  in  the  opposite  direction.  Hence,  the  forces 
being  equal  and  in  opposite  directions,  no  motion  is  produced. 


How  do  birds  fly?  How  is  a  boat  propelled  by  the  oar?  When  two 
bodies  meet,  which  receives  the  greater  shock?  What  other  illustrations 
of  action  and  reaction  ?  Why  can  not  several  men  standing  in  a  boat  move 
it  through  the  water  by  pushing  against  the  side  ? 


THIRD     LAW     OF     MOTION.  53 

According  to  this  law,  all  attempts  to  produce  perpetual  motion 
must  necessarily  fail,  because,  by  whatever  force  a  body  is  set  in 
motion,  there  is  always  an  equal  tendency  to  an  opposite  motion. 
If  a  man  should  step  into  a  basket,  and  attempt  to  lift  himself 
by  taking  hold  of  the  handle,  he  would  find  that  if  he  lifted  up 
two  hundred  pounds,  he  would  be  obliged,  in  order  to  do  it,  to 
press  down  upon  the  bottom  of  the  basket  just  two  hundred  pounds, 
and  hence  he  would  remain  stationary. 

In  observing  the  motion  of  bodies,  we  have  noticed  three  par- 
ticulars :  time,  space,  and  velocity,  that  is,  the  time  any  body  is 
moving,  the  space  it  passes  over,  and  the  rapidity  of  its  motion, 
or  its  velocity. 

If  the  body  pass  over  equal  spaces  in  equal  times,  it  is  said 
to  move  with  uniform  velocity.  Thus,  if  a  man  travel  thirty 
miles  at  the  rate  of  five  miles  an  hour,  he  travels  with  uniform 
velocity. 

If  the  spaces  over  which  a  body  passes  are  constantly  increas- 
ing, it  is  said  to  move  with  an  accelerated  velocity.  Thus,  when 
a  stone  rolls  down  the  side  of  a  mountain,  its  velocity  constantly 
increases  until  it  reaches  the  base. 

If  its  velocity  increases  equally  at  each  successive  instant  of 
time,  it  is  said  to  move  with  uniformly  accelerated  velocity. 
This  is  nearly,  though  not  strictly,  the  condition  of  bodies  falling 
toward  the  earth  under  the  influence  of  gravity. 

But  if  the  spaces  over  which  a  body  moves  in  equal  times  con- 
tinually diminish,  it  is  said  to  move  with  a  retarded  velocity  ; 
and  if  its  velocity  diminishes  equally  at  each  instant  of  time,  the 
body  has  a  uniformly  retarded  velocity.  This  is  illustrated  in 
throwing  any  body  into  the  air :  its  velocity  continually  decreases 
until  it  finally  stops,  and  returns  to  the  earth  with  a  velocity 
which  may  be  regarded  as  uniformly  accelerated. 

On  comparing  time,  space,  and  velocity,  we  shall  be  ena- 
bled to  derive  several  highly  important  truths.  Thus,  for  ex- 
Why  is  perpetual  motion  near  the  earth  impossible  ?  Where  is  it  pos- 
sible ?  What  three  things  are  to  be  particularly  noticed  in  observing  the 
motions  of  bodies  ?  Describe  accelerated  and  retarded  velocities.  Uni- 
formly accelerated  and  retarded  velocities. 


54  NATURAL    PHILOSOPHY. 

ample,  it  is  evident  that  if  the  time  during  which  any  body  is 
moving  over  a  given  space  be  diminished,  the  velocity  must  be 
increased ;  and  if  the  time  is  increased,  or  the  body  has  a  longer 
time  to  move,  it  must  move  slower,  or  its  velocity  must  be  di- 
minished. 

In  other  words,  if  the  space  is  given,  the  time  will  be  inversely 
as  the  velocity. 

1.  The  space  over  which  any  body  moves  will  always  be  equal 
to  the  time  multiplied  into  the  velocity ;  or,  if  S  =  the  space, 
T  =  the  time,  and  V  =  the  velocity,  then  S  =  T  x  V.     For  it  is 
evident  that  the  space  to  be  passed  over  will  be  measured  by 
the  time  the  body  moves,  multiplied  by  the  rate  at  which  it 
moves. 

Thus,  for  example,  at  the  rate  of  five  miles  per  hour,  how  far 
will  a  man  travel  in  six  hours  ?  Ans.,  30  miles.  Six  hours  is 
the  time  ;  multiply  this  by  five,  the  velocity,  and  it  equals  thirty 
miles,  the  space. 

2.  The  time  will  equal  the  space  divided  by  the  velocity,  or 
c 

T=— .    For  example,  how  long  will  it  take  a  man  to  travel  thirty 

miles  at  five  miles  per  hour  ?  Ans.,  six  hours.  This  is  obtained 
by  dividing  the  space,  thirty  miles,  by  five,  the  velocity,  and  it 
equals  six,  the  time. 

3.  The  velocity  equals  the  space  divided  by  the  time,  or, 

S 
V  =: For  example,  a  man  travels  thirty  miles  in  six  hours, 

at  what  rate  must  he  travel  ?  Ans.,  five  miles  per  hour.  This 
is  obtained  by  dividing  the  space,  thirty  miles,  by  six,  the  time, 
and  it  is  equal  to  five,  the  velocity. 

It  will  be  noticed  that  when  different  times,  spaces,  and  ve- 
locities are  compared,  instead  of  "equals,"  in  the  above  cases,  we 
may  read  "  varies  as." 

Thus  the  velocity  varies  as  the  space  divided  by  the  time. 

We  have  also  seen  that  the  quantity  of  motion  or  momentum 
of  a  body  was  measured  by  the  quantity  of  matter  multiplied 

Mention  the  three  equations  of  time,  space,  and  velocity. 


THIRD     LAW     OF     MOTION.  55 

into  the  velocity ;  or,  in  other  words,  if  M  represent  the  momen- 

M 

turn,  and  Q  the  quantity  of  matter,  M  =  QxV,  and  Q= — , 

V 

V  =  ??.     That  is, 
Q 

1 .  The  momentum  is  equal  to  the  quantity  of  matter  multi- 
plied by  the  velocity  ;  or,  when  different  momenta  are  compared, 
varies  as  Q  X  V. 

2.  The  quantity  of  matter  is  equal  to  the  momentum  divided  by 

M 

the  velocity,  or  Q  =  — 

3.  The  velocity  is  equal  to  the  momentum  divided  by  the  quan- 

TVT 

tity  of  matter,  or  V  =  — . 

Q 

4.  With  a  given  quantity  of  matter,  as  a  pound  or  a  ton,  the 
momentum  will  vary  as  the  velocity ;  or,  the  faster  the  body 
moves,  the  greater  its  momentum. 

5.  With  a  given  velocity,  the  momentum  will  vary  as  the 
quantity  of  matter  ;  for,  the  larger  the  body  is,  the  greater  the  ob- 
stacle it  will  overcome. 

6.  In  two  bodies,  whose  velocities  are  inversely  as  their  quan- 
tities of  matter,  the  momenta  will  be  equal.     Thus,  if  a  ten 
pound  ball  move  ten  feet  per  second,  its  momentum  will  just 
equal  a  one  pound  ball  moving  one  hundred  feet  per  second  ; 
hence  the  smallest  body  may  be  made  to  stop  or  to  put  in  motion 
the  largest  body,  provided  its  velocity  be  as  much  greater  as  its 
matter  is  less. 

It  is  necessary  in  all  these  calculations  to  fix  upon  a  unit  of 
time  and  of  measure ;  one  second  is  taken  for  the  unit  of  time, 
and  one  foot  is  generally  taken  as  a  unit  of  measure. 

PROBLEMS. 

1 .  A  sixty-four  pound  cannon  ball  was  fired  against  a  fort  with 
a  velocity  of  2000  feet  per  second.     What  was  the  force  with 
which  it  struck  ? 

Ans.,  128,000  Ibs. 

2.  A  square  block  of  stone,  weighing  500  pounds,  was  just 


hQ  NATURAL    PHILOSOPHY. 

equal  to  resist  the  action  of  a  cannon  ball  moving  at  the  rate  of 
1500  feet  per  second.     What  was  the  weight  of  the  ball  ? 

Am.,  i  Ib. 

3.  A  battering  ram,  weighing  200  pounds,  was  forced  againsl 
the  walls  of  a  fortified  town,  and  overcame  a  resistance  of  twenty 
tons.  What  was  the  velocity  with  which  it  moved  ? 

Ans.,  200  feet  per  second. 

SECTION  EI. COMPOSITION  AND  RESOLUTION  OF  MOTION  AND  FORCES. 

When  a  body  is  acted  upon  by  two  forces,  it  will  move  in  a 
direction  which  is  called  the  resultant  of  the  tivo  forces. 

1.  If  the  forces  are  equal,  and  at  right  angles  to  each  other , 
the  body  will  describe  the  diagonal  of  a  square  ;  but 

2.  If  the  forces  are  unequal,  it  will  describe  the  diagonal  of 
a  rectangle. 

3.  If  the  forces  act  either  at  acute  or  obtuse  angles,  the  body 
will  describe  the  diagonal  of  a  parallelogram. 

4.  If  a  body  be  acted  upon  by  three  or  more  forces,  its  direc- 
tion  may  be  represented  by  a  single  force,  which  is  the  resultant 
of  them  all. 

5.  If  any  body  is  acted  upon  at  the  same  time  by  a  constant 
and  a  variable  force,  it  will  describe  a  curve. 

A  single  force  may  also  be  resolved  into  several  other  forces, 
acting  in  different  directions. 

HITHERTO  we  have  considered  the  motions  which  were  pro- 
duced by  a  single  force.  But  most  of  the  motions  with  which 
we  are  familiar  are  the  result  of  two  or  more  forces,  and  the  prob- 
lem to  determine  the  direction  any  body  will  take,  moving  under 
the  influence  of  several  forces,  which  act  in  different  directions, 
is  called  the  problem  of  the 

Composition  of  Forces. — When  two  forces  act  upon  any  body, 
as  the  forces  e/upon  the  ball  A,  Fig.  23,  at  right  angles  to  each 
other,  and  with  equal  power,  the  body  will  move  between  them 
thus : 

What  is  meant  by  the  composition  of  forces?  What  figures  represent 
tije  action  of  two  forces  ? 


COMPOSITION    OF    FORCES. 


57 


-  23-  1 .  If  the  force  e  would  cause  the  ball  to 

move  to  B  in  one  minute  of  time,  and  the 
force /would  make  it  move  in  the  same 
time  to  C,  the  body  will  obey  both  forces, 
and  move  between  them  in  the  direction 
A  D.  It  will  describe  the  diagonal  of  a 
square,  and  will  be  found  at  the  end  of  one 
minute  at  D  ;  and  a  force,  acting  in  the 
D  direction  AD,  which  would  cause  the 
body  to  move  to  D  in  the  same  time  that 
both  forces  would  produce  the  same  effect,  is  called  the  resultant. 

2.  If  the  forces  act  as  before,  but  one  of  them  is  greater  than 
the  other,  the  body  will  describe  the  diagonal  of  a  rectangle ;  thus, 
let  the  force  e,  Fig.  24,  be  twice  that  off;  then  the  ball  will  de- 

Fig.  24.  scribe  the  diagonal  A  D ;  and  the 

greater  the  difference  between  the 
two  forces,  the  nearer  will  the 
lines  A  B,  C  D  approach  each  oth- 
er, or  the  longer  will  be  the  rect- 
angle  in  proportion  to  its  width. 

3.  If  the  forces  act  at  oblique  or  at  acute  angles  to  each  other, 

as  e  b,  upon  the  ball  A,  Fig.  25, 
then  the  ball  will  describe  the 
diagonal  of  a  parallelogram,  A  D, 
and  will  be  found  at  D  in  the 
same  time  that  would  be  required 
to  carry  it  to  B  or  C  by  either 
force  acting  singly. 

4.  If  a  body  is  acted  upon 
by  three  or  more  forces,  it  is 
easy  to  reduce  them  to  one 
force,  and  hence  to  determ- 
ine the  direction  which  the 
body  will  take.  Thus,  sup- 
pose the  ball  A,  Fig.  26,  to 
be  acted  upon  by  four  forces, 
abed.  If  the  ball  move 
under  the  influence  of  a  and 
b,  it  will  be  found  at  C,  or 
the  resultant  of  the  two 
forces  would  act  in  the  di- 
rection of  A  C.  If  the  ball 


Fig.  25. 


Illustrate  by  the  diagrams  the  action  of  several  forces. 
C2 


58  NATURAL    PHILOSOPHY. 

is  moved  by  this  resultant  and  the  force  c,  it  will  be  found  at  E, 
or  the  force  will  act  in  the  direction  of  A  C.  Finally,  if  the  ball 
move  under  the  influence  of  this  latter  resultant  and  d,  it  will  be 
found  at  F ;  or  if  it  be  acted  upon  by  all  the  four  forces  at  the 
same  time,  it  will  describe  the  line  A  F  in  the  same  time  that 
either  force  singly  would  have  carried  it  to  either  of  the  sides  of 
the  three  parallelograms. 

By  inspecting  the  diagrams  above,  the  following  truths  become 
obvious : 

1.  When  two  forces,  acting  separately,  would  cause  a  body  to 
describe  the  two  sides  of  a  triangle,  when  acting  together  they 
will  cause  it  to  describe  the  third  side.     This  is  evident  from 
Fig.  26.     Any  two  of  those  forces,  as  a  b,  acting  together,  since 
the  side  B  C  is  equal  to  A  D,  would  cause  a  body  to  describe  the 
third  side,  A  C,  of  the  triangle  ABC. 

2.  If  a.  body  be  acted  upon  by  several  forces,  represented  by  all 
the  sides  of  a  polygon  but  one,  the  resultant  will  describe  the 
last  side.     Thus,  abed,  Fig.  26,  represents  the  four  forces 
acting  upon  A.     The  sides  A  B,  B  C,  C  E,  and  E  F,  also  rep- 
resent these  forces.     By  their  joint  action,  the  body  will  describe 
the  remaining  side,  A  F. 

3.  Any  number  offerees,  acting  in  an  indefinite  number  of  di- 
rections, may  all  be  represented  by  one  force,  the  resultant  of  them 
all,  acting  in  a  single  direction.     Hence,  if  any  body  is  acted 
upon  by  three  forces,  represented  by  three  sides  of  a  triangle,*  as 
A  B,  B  C,  and  C  A,  it  will  remain  at  rest ;  and  if  it  be  acted 
upon  by  a  number  of  forces,  represented  by  the  sides  of  a  polygon, 
it  will  also  remain  at  rest ;  and,  finally,  if  a  body  be  acted  upon 
by  opposite  and  equal  forces,  it  will  remain  at  rest.     This  may 
be  called  the  equilibrium  offerees. 

In  all  these  cases  it  is  assumed  that  the  motion  is  of  uniform 
velocity.  But,  suppose  a  body  be  acted  upon  by  two  or  more 
forces,  one  of  which  is  variable,  then  the  body  will  not  describe 
a  straight  line,  but  a  curve.  This  curve  will  be  examined  under 
Central  Forces. 

*  Taken  in  order. 

Mention  the  several  truths  derived  from  the  composition  of  forces.  What 
direction  will  a  body  take  acted  upon  by  two  forces,  one  of  which  is  variable  T 


RESOLUTION    OF    FORCES. 


Resolution  of  Forces. — The  resolution  offerees  is  just  the  op- 
posite process  to  their  composition.  By  the  former  several  forces 
are  reduced  to  one,  and  by  the  latter  one  force  is  resolved  into 
two  or  more,  acting  in  different  directions. 


Fig.  27. 


Thus,  suppose  that  a  ball  be 
propelled  by  a  force,  Fig.  27,  so 
that  in  a  given  time  it  shall  reach 
D  the  point  B.  This  force  may  be 
resolved  into  two,  acting  in  the  di- 
rection A  E  and  A  D,  or  into  four, 
acting  in  the  directions  abed. 

Many  illustrations  are  found  in 
nature  and  art  of  the  composition 
and  resolution  of  forces,  hi  which  bodies  are  acted  upon  by  sev- 
eral forces,  and  the  results  are  always  conformable  to  the  princi- 
ples above  laid  down.  Thus,  a  ship  sails  under  the  influence  of 
two  forces,  which  may  be  reduced  to  one. 

In  Fig.  28,  let  the  direction  of  the  ship  be  a  b,  the  sail  c  e,  and 
the  direction  of  the  wind  f  e.  Now  the  force  of 
the  wind,  represented  by  the  line  g  e,  may  be  re- 
solved into  p  g  and  e  p.  The  part  e  p  acting  par- 
allel to  the  direction  of  the  sail,  e  c,  does  not  pro- 
pel the  vessel  at  all,  but  the  force  g  p  is  the  only 
force  which  causes  it  to  move.  The  force  g  p 
acts  obliquely,  and  must  be  resolved  into  g  i  and 
i  p.  The  force  g  i  is  equal  to  the  action  of  the 
water  on  the  keel  of  the  vessel,  and  the  force  i  p 
represents  the  force  of  the  wind  in  the  direction 
which  the  ship  sails.  It  is  evident  that  two  ships 
may  sail  in  exactly  opposite  directions  with  the 
same  wind. 

A  kite  ascends  under  the  influence  of  three  forces  :  the  wind, 
the  string  by  which  it  is  held,  and  the  kite  itself,  and  it  always 
moves,  in  accordance  with  the  laws  above  stated,  in  a  direction 
which  is  the  resultant  of  these  forces. 


Fig.  28. 

b 


What  is  meant  by  the  resolution  of  forces?     Explain  the  diagram, 
illustrations  of  the  composition  and  resolution  of  forces  ? 


What 


60  NATURAL  PHILOSOPHY. 

PROBLEMS. 

A  carrier  pigeon  flew  directly  west  twenty  miles  per  hour  for 
five  hours,  and  a  wind  from  the  north  carried  her  toward  the 
south  at  the  same  rate.  What  figure  would  represent  the  space 
she  passed  over,  and  what  distance  would  she  be  from  the  place 
of  starting  at  the  end  of  five  hours  ?  Ans.,  141.42  miles. 

A  vessel  sailed  from  New  York,  steering  directly  south  for  ten 
days,  at  the  rate  of  one  hundred  miles  each  day,  while  the  west- 
erly winds  drove  her  directly  east  at  the  rate  of  fifty  miles  a  day. 
What  kind  of  figure  will  represent  the  space,  and  at  what  dis- 
tance will  the  ship  be  from  New  York  ? 

Ans.,  1118-f-  miles. 

What  would  be  her  latitude  and  longitude,  New  York  being 
in  latitude  41°  ? 

SECTION  IV.— GRAVITATION.    VARIABLE  FORCES  AND  MOTIONS. 

All  bodies  near  the  earth's  surface  are  under  the  influence  of 
gravity,  a  force  which  is  constantly  repeated,  and  hence  gives 
rise  to  variable  motions.  Bodies  falling  toward  the  earth  con- 
stantly increase  in  velocity,  and  the  laivs  which  govern  their  de- 
scent or  ascent  are  called  the 

I.  Laws  of  Falling  Bodies.  The  space  which  a  falling  body 
describes  may  be  represented  by  a  triangle,  as  that  of  uniform 
motion  is  by  a  rectangle. 

I .  The  great  law  of  falling  bodies  is,  tJiat  the  spaces  they  de- 
scribe are  as  the  squares  of  the  times  during  which  they  are 
falling. 

II.  Every  body  has  a  certain  point  called  the  center  of  grav- 
ity :  if  this  point  is  supported,  the  whole  body  will  be  at  rest ;  if 
it  is  moved,  the  whole  body  ivill  move  ;  and  if  it  is  not  support- 
ed, the  body  will  fall. 

III.  Bodies  moving  around  an  immovable  center,  tend  to 
move  in  a  tangent  to  the  curve,  and  the  force  generated  by  their 
revolution  is  called  tangential  or  centrifugal.      This  force  is 
great  or  small,  according  to  the  size  of  the  body,  its  distance 

from  the  axis  of  revolution,  and  the  velocity  with  which  it  moves. 


GRAVITATION.  61 

IV.  Wlien  ladies  impinge  upon  each  other,  they  give  and  re- 
ceive the  same  amount  of  motion.  1 .  Inelastic  bodies,  after  im- 
pact, move  ivith  such  a  velocity  that  the  sum  of  their  united  mo- 
menta just  equals  the  sum  of  their  separate  momenta  previous 
to  impact. 

2.  Elastic  bodies,  when  they  impinge  upon  each  other,  give 
znd  receive  double  the  shock  that  they  would  if  inelastic. 

IN  the  motion  of  bodies  hitherto  considered,  we  have  regarded 
them,  with  a  single  exception,  as  moving  over  equal  spaces  in 
equal  times,  under  the  influence  of  a  force  which  is  imparted  for 
once  only,  and  the  motion  thus  generated  necessarily  becomes 
uniform. 

But  there  are  variable  forces,  and,  of  course,  variable  motions. 
When  a  body  is  acted  upon  by  a  force  which  is  repeated  at  every 
instant  of  time,  the  motion  of  it  is  constantly  increasing,  and  its 
velocity  is  uniformly  accelerated.  The  attraction  of  gravita- 
tion, in  respect  to  bodies  near  the  earth,  may  be  considered,  with- 
gut  material  error,  as  repeated  at  each  instant  of  time,  and  hence 
a  body  drawn  toward  the  center  of  the  earth  constantly  increases 
in  velocity.  The  laws  which  govern  the  ascent  and  descent  of 
bodies  from  and  to  the  earth  are  called 

I.  The  Laws  of  Falling  Bodies. — These  laws  may  be  demon- 
strated and  illustrated  by  means  of  diagrams,  and  proved  by  ex- 
periments. 

1.  Illustration. — In  uniform  motion  we 
have  seen  that  the  space  equals  the  time  mul 
tiplied  into  the  velocity.  If,  therefore,  one  side 
of  a  rectangle,  A  B,  Fig.  29,  represent  the  ve 
locity  with  which  a  body  moves,  and  A  1  2  3 
C  the  several  instants  of  time  it  is  moving 
the  figure  A  C  D  B  will  represent  the  space  il 
will  pass  over,  and  hence  a  rectangle  is  a  prop- 
er representation  of  uniform  motion. 

But  when  the  force  acts  so  as  to  produce  a  uniformly  accel- 
erated motion,  we  must  find  a  different  figure.  Suppose  a  force 

How  are  variable  motions  produced  ?  How  does  the  force  of  gravitation 
act  ?  What  figure  represents  uniform  motion  ? 


62 


NATURAL    PHILOSOPHY. 


be  repeated  upon  a  body  three  times  during  its  motion,  what  kind 
of  a  figure  would  represent  the  space  it  would  describe  ? 

Let  the  space  in  the  first  impulse  be  represented  by  a  rectan- 
gle, Fig.  30,  as  before,  A  B  C  1,  A  I  F&.ao. 
the  time,  and  A  B  the  velocity.     At  1  let    A  -R 
the  force  be  repeated,  and  as  it  is  under 
the  influence  of  twice  the  force,  its  veloc- 
ity will  be  doubled,  and  the  next  instant  ^ 
it  will  describe  the  figure  1  2  E  D.     On 
repeating  the  force  at  2,  its  velocity  will  2 
be  tripled,  and  the  figure  2  3  G-  F  will 
be  described.     Now,  if  we  consider  the 
force  as  repeated  constantly  from  A  to  3, 
the  space  described  will  be  represented  by  the  triangle  A  3  G. 

Gravity  is  such  a  force,  and  hence  we  may  represent  the  time 
a  body  is  falling  by  one  side  of  a  right-angled  triangle,  and  the 
last  acquired  velocity  by  the  other,  while  the  triangle  itself  will 
represent  the  space  which  a  body  passes  over. 

If  we  compare  the  spaces  described  by  any  body  during  sev- 
eral seconds  of  time,  we  shall  jind  them  to  be  as  the  squares  of 
the  times. 

Thus,  let  A  B  C  and  ADE,  Fig.  31,  represent  the  spaces  de- 
scribed in  two  seconds  of  time,  A  B  and  A  D.  _    31 
The  two  triangles  are  similar,  and  we  obtain 
the  proportion  ABC  :  ADE  :  :  AB2 :  AD2 ;  or 
as  BC2 :  DE2.* 

Since  the  spaces  are  to  each  other  as  the 
squares  of  the  times,  if  the  times  or  number 
of  seconds  during  which  a  body  is  falling  from 
a  state  of  rest  under  the  influence  of  gravity 
be  as  the  numbers  1,  2,  3,  4,  5,  &c.,  then  the  r 
spaces  may  at  once  be  determined  by  simply  squaring  the  times, 
1,4,  9,  16,  25,  &c.  If,  therefore,  we  can  ascertain  how  far  a 
*  This  is  on  the  principle  that  similar  triangles  are  to  each  other  as  the 
squares  of  their  homologous  sides.  By  another  principle  we  have  AB  X  BC 
to  AD  X  DE,  as  the  triangles  themselves. 

What  figure  may  represent  bodies  moving  to  or  from  the  earth  under 
the  influence  of  gravity?  What  relation  do  the  spaces  and  times  bear  to 
each  other  when  bodies  fall  freely  under  the  influence  of  gravity  ?  If  the 
times  are  1,  2,  3,  4,  what  numbers  will  represent  the  spaces  ? 


LAWS    OF    FALLING    BODIES.  63 

body  will  fall  during  the  first  second,  it  will  be  easy  to  determ- 
ine that  of  all  the  rest.  It  has  been  found  by  experiment  that 
near  the  earth's  surface  a  body  falls  16^  feet  in  a  second,  and 
hence  it  would  fall  in  two  seconds  four  times  as  far,  or  64£  feet ; 
in  three  seconds,  nine  times  as  far,  or  144f  feet ;  in  four  seconds, 
sixteen  times  as  far,  or  2571  feet. 

This  may  be  shown  in  a  different  manner.  Thus,  at  the  end 
of  one  second,  the  velocity  generated,  if  gravity  were  to  cease  its 
action,  would  be  sufficient  to  carry  it  during  the  next  second 
feet;  but  as  gravity  acts  constantly,  it  will  cause  it  to  fall 
feet  further,  which  being  added,  makes  48T32-  feet  for  the  second 
instant ;  and  now  it  has  acquired  a  velocity  which  will  carry  it 
64T4^  feet  during  the  third  second,  while  gravity  will  carry  it 
16y~  further^:  80—  feet ;  and  the  fourth  second,  by  the  same 
law,  it  will  fall  1 12T72  feet.  If  we  examine  the  numbers,  we 
find  them  to  be  16T^,  48T8¥,  80-&,  112T\,  which  represent  the 
spaces  for  each  successive  second  of  time,  and  we  shall  observe 
that  they  are  as  the  numbers  1,  3,  5,  7,  9,  &c. 

If  we  add  to  each  the  space  previously  passed  over,  we  shall 
find  uiey  are  as  the  squares  of  the  times.  Thus  the  first  and 
second  second  make  64T4¥,  or  the  square  of  2  z=  4  X  16^  ;  add  the 
third  second,  and  it  will  equal  9X  16T^  =  144T9^  ;  and  adding 
the  fourth  second,  it  will  equal  257  T4T.  Hence,  if  the  times  are 
as  1,  2,  3,  4,  &c.,  then  the  spaces  are  as  1,4,  9,  16,  &c.,  and  the 
spaces  for  each  second  as  1,  3,  5,  7,  9,  11,  &c. 

2.  This  law,  so  readily  demonstrated  by  figures  and  numbers, 
may  be  proved  experimentally  by  means  of 

Atwood's  Machine. — The  arrangement  is  such  in  this  appa- 
ratus that  the  body  descends  much  slower  than  if  it  were  wholly 
under  the  influence  of  gravity,  and  yet  the  relation  between  the 
times  and  spaces  is  perfectly  preserved.  Thus,  Fig.  32,  the 
weights  m  n  are  exactly  balanced,  and  weigh  31^  ounces  each, 
so  that  both  of  these  weigh  63  ounces.  If,  now,  a  weight  of 
one  ounce  be  placed  on  one  of  these  weights,  it  will  carry  down 

How  far  does  a  body  fall  under  the  influence  of  gravity  in  one  second  ? 
What  velocity  does  it  acquire  the  first  second,  and  what  the  second  second  ? 
What  series  of  numbers  represent  the  spaces  passed  over  by  a  body  in  each 
successive  second  of  timel  Describe  the  principle  of  Atwood's  Machine. 


NATURAL    PHILOSOPHY. 


one  31|-  ounces,  and  cause  the  other  31^ 
ounces  to  rise,  so  that  the  whole  amount  of 
matter  in  motion  is  64  ounces.  If  the  one 
ounce  fell  freely,  it  would  fall  IGy^  feet  in 
a  second ;  but  as  it  has  64  ounces  to  move, 
it  will  fall  but  one  sixty-fourth  as  fast :  16^3- 
feet  reduced  to  inches  equals  192  inches,* 
a  sixty-fourth  part  of  which  is  three  inches. 
The  first  second  the  weight  would  fall  3 
inches ;  in  two  seconds  it  would  fall  freely 
768  inches,  one  sixty-fourth  of  which  is  12 
inches  ;  a  third  second  27  inches,  a  fourth 
48  inches,  a  fifth  75,  a  sixth  108  =  9  feet. 
Hence,  by  this  machine,  a  body  which,  by 
falling  freely,  would  descend  576  feet  in  six 
seconds  of  time,  would  only  fall  nine  feet. 


Fig.  32. 


Seconds    .     . 

1 

2 

3 

4 

5 

Gravity,  feet  . 

16rV 

64^ 

144f 

2571 

402TV 

Atwood's  Ma-  )  • 
i  •                 /*  in* 
chine     .     .  J 

3 

12 

27 

48 

75 

There  is  some  friction  to  be  overcome,  yet 
when  this  theory  is  subjected  to  the  test  of  experiment,  the 
weights  are  found  to  fall  in  exact  obedience  to  it.  There  is  a 
pendulum,  and  clock-work  attached,  which  beats  seconds,  and 
some  other  parts  not  fully  represented. 

In  proving  the  above  laws  experimentally,  two  small  weights, 
i  c,  are  applied  to  n,  one  of  which  will  pass  through  the  ring, 
and  the  other  will  be  taken  off  by  it. 

(1  .)  To  prove  that  the  spaces  passed  over  are  as  the  squares  of 
the  times, 


.  —  Place  n  at  c,  and  lay  the  one  ounce  weight,  i,  upon  it.  If  now 
the  slide  b  is  placed  three  inches  from  c,  and  the  weight  allowed  to  fall, 
it  will  reach  the  slide  in  one  second.  Then  place  the  slide  one  foot  from 
c.  and  the  weight  will  reach  it  in  just  two  seconds;  in  three  seconds  it  will 
fall  27  inches,  and  in  four  seconds  48  inches.  The  spaces  are  as  the  squares 

of  the  times,  ?'  ^'  ?'  ,4r.     The  time  is  measured  by  the  pendulum,  which 

17  *1?  i/j   10 

beats  seconds. 

*  Omitting  the  fraction  T\j. 


LAWS    OF    FALLING    BODIES.  65 

(2.)  To  determine  the  velocity  acquired  at  the  end  of  each  sec- 
ond, and  the  distance  passed  over  in  each  successive  instant  of 
time. 

Exp. — Place  the  weight  e  on  n,  and  place  the  brass  ring  a  three 
inches  from  c ;  on  letting  the  weight  fall,  it  will  arrive  at  the  ring  in  one 
second ;  the  weight,  e,  is  now  taken  off  by  the  ring,  and  the  velocity  ac- 
quired will  carry  it  six  inches  the  next  second ;  its  velocity,  therefore,  at 
the  end  of  the  first  second,  is  sufficient  to  carry  it  twice  the  distance  in  the 
same  time,  and  the  apace  passed  over  during  the  next  second  will  be  nine 
inches,  if  the  load  remain  attached.  If  the  slide  be  placed  twelve  inches 
from  c,  and  the  weight  fall  two  seconds  before  the  load  is  taken  off,  its  ac- 
quired velocity  will  carry  it  down  twelve  inches  the  third  second;  hence, 
if  the  load  had  not  been  taken  off,  the  space  passed  over  would  have  been 
fifteen  inches.  It  is  evident  that  the  spaces  3,  9,  15  are  obtained  by  mul 
tiplying  the  numbers  1,  3,  5  into  the  distance  which  the  weight  fell  tho 
first  second,  or  by  three. 

The  weights  m  n  may  be  varied  at  pleasure,  and  also  the 
loads  i  e;  the  smaller  the  load  in  respect  to  the  weight,  the 
slower  the  motion,  but  the  laws  are  the  same. 

In  nature  we  have  numerous  illustrations  of  bodies  falling  with 
a  constantly  accelerated  motion,  as  when  any  mass  slides  down 
an  inclined  plane,  or  a  stone  rolls  down  the  side  of  a  mountain, 
but  the  law  is  the  same.  Few  bodies  fall  perpendicularly. 
Rain-drops*  and  hail  sometimes  acquire  considerable  velocity  ;  the 
latter  frequently  breaks  panes  of  glass  and  destroys  vegetation. 
Meteoric  stones,  falling  from  great  heights,  acquire  such  velocity 
as  to  bury  themselves  in  the  earth.  The  blow  of  a  sledge  or 
hammer  is  greatly  increased  by  the  distance  through  which  it 
falls.  The  logs  which  slide  down  the  wooden  troughs  from  the 
Alpine  heights  acquire  a  velocity  which  seems  almost  incredible. 

3.  When  a  body  is  thrown  perpendicularly  upward,  its  motion 
is  constantly  retarded,  under  the  influence  of  gravity,  until  it 
stops  and  returns  again  to  the  earth,  and  in  this  case  the  law  is 
reversed ;  that  is,  if  it  be  projected  with  a  velocity  which  it 
would  gain  by  falling  six  seconds,  it  will  rise  to  the  height  from 
which  it  must  fall  to  gain  that  velocity  ;  but  the  spaces  for  each 
instant  will  be  reversed,  and  we  should  have,  instead  of  the  se- 
ries 1,  3,  5,  7,  9—9,  7,  5,  3,  1. 

What  illustrations  in  nature  of  the  laws  of  falling  bodies  ?  What  is  the 
law  when  bodies  are  thrown  perpendicularly  upward  ?  What  kind  of  mo- 
tion does  such  a  body  describe  ? 


66  NATURAL    PHILOSOPHY. 

In  consequence  of  the  relation  of  a  rectangle  to  a  right-angled 
triangle,  the  latter  being  half  of  the  former,  the  one  representing 
uniform  motion,  and  the  other  accelerated  motion,  it  is  easy  to 
Bee  that  a  body  moving  uniformly  with  a  velocity  equal  to  that 
which  a  falling  body  acquires  in  a  given  time,  would  describe 
twice  the  space  in  the  same  time,  and  also  that  a  body  moving 
directly  upward  uniformly  with  the  velocity  it  may  acquire  in 
falling  from  a  given  height,  will  describe  double  the  space  it 
would  under  the  retarding  influence  of  gravity. 

It  is  also  evident,  that  a  body  projected  downward  from  a  given 
point,  will  describe  a  space  equal  to  that  described  by  a  body 
falling  during  the  same  time,  and  one  moving  uniformly  with  the 
velocity  of  projection.  If  it  be  thrown  upward,  the  space  will  be 
the  difference  between  a  body  moving  uniformly  with  the  veloc- 
ity of  projection  for  the  time,  and  a  body  falling  freely  during  the 
same  time. 

For  those  acquainted  with  algebra  and  geometry,  the  following  repre- 
sentations of  the  relations  of  time,  space,  and  velocity  are  highly  important. 

Let  g-=:the  space  which  a  body  falls  during  one  second  of  time  =16^-  feet. 
2^:=the  velocity  acquired  at  the  end  of  one  second. 
S=the  space  described  by  the  body  in  any  given  time,  as  T,  and 
V—  -the  velocity  acquired  in  the  time,  T.     Then,  since  the  spaces  are 
as  the  squares  of  the  times, 

&'.g::  Ta:  I2,  or.     .     .     .  Sr=g-T2; 

also,  S:#::V':(^)2,or.     .     .  S=, 

and  V2=%S,  or  ......  V 

but  1  :  Zg  :  :  T  :  V  •.•   .     .     .     .  V=2gT. 

As  V=2^T.-  .......  T~; 


and  as  S=*T«  •.•     ...... 

These  formula?  may  be  employed  in  the  solution  of  the  following 

PROBLEMS. 

1.  What  space  will  a  body  fall  through  in  ten  seconds,  and  what  velocity 
will  it  acquire  ? 

The  space,  S  =  g-Ta,  g  =  16^  feet.  The  square  ofT  =  10XlO=100 
X16TV=1608  feet,  Ans.  Velocity,  V  =  2g>xT  =  2Xl6T1I  X  10=321§ 
feet,  Ans. 

2.  How  long  would  a  stone  be  in  falling  from  the  top  of  the  great  pyra- 

What  relations  do  the  spaces  described  by  uniform  motion  bear  to  those 
described  by  falling  bodies  ? 


CENTER    OF    GRAVITY.  67 

raid  in  Egypt  to  the  base,  a  distance  of  500  feet,  and  vfrhat  velocity  would 
it  acquire  ? 

Ans.,  T  =  5.5756,  arid  velocity  =  179.3485  feet  per  second. 

3.  To  what  height  would  a  ball  ascend,  shot  directly  upward  with  a  ve- 
locity of  2000  feet  per  second  ? 

Ans.,  62176+  feet. 

4.  If  it  was  twenty  seconds  before  the  ball  returned,  to  what  height  did 
it  reach,  and  with  what  velocity  was  it  projected  ? 

Ans.,  Height,  1608^  feet;  velocity,  321^  feet  a  second. 

5.  A  cannon  ball  let  fall  from  the  top  of  a  tower  was  four  seconds  in 
reaching  its  base.     What  was  the  height  of  the  tower  ? 

Ans.,  257£  feet. 

6.  If  a  ball  is  projected  downward  with  a  velocity  of  twenty  feet  a  sec- 
ond, how  far  will  it  fall  in  ten  seconds? 

The  velocity  given  to  the  ball  will  be  uniform,  and  will  be  equal  to  T  X  V, 
or  10x20  =  200,  and  the  space  which  the  ball  will  describe  under  the  in- 
fluence of  gravity  will  be  =  g-T2,  or  16T^X  100  =  I608j  feet. 

Ans.,  1608  1-  +  200  =  1  808  £  feet. 

To  determine  the  spaces  described  by  any  body  in  one  or  more  seconds 
during  its  fall,  we  have  only  to  refer  to  the  law,  where  the  spaces  described 
in  equal  successive  times  are  as  the  odd  numbers  1,  3,  5,  7,  9,  &c.  The 
space  for  the  first  second  is  g  feet,  the  second  second  3g  feet,  third  second 
5g  feet,  &c. 

7.  A  body  fell  eight  seconds.     How  far  did  it  fall  the  third  second  ?  how 
far  the  fifth  second  ?  and  how  far  the  last  ? 

Ans.,  Third  =  80T52  feet;  fifth  =  144£;  eighth  =2411 

8.  An  aeronaut,  after  ascending  23  16  feet,  found  it  necessary  to  throw  out 
a  bag  of  sand.     What  space  would  it  describe  during  the  last  second  of  its 
fall? 

Ans.,  369}|  feet- 


II.  Center  of  Gravity.  —  The  force  of  gravitation,  acting  on  a 
mass  of  atoms,  tends  to  draw  them  all  toward  the  center  of  the 
earth  in  lines,  which  for  small  distances  may  be  regarded  as  par- 
allel. The  atoms  of  a  mass  one  foot  square  all  tend  toward 
the  center  of  the  earth  in  lines  so  nearly  parallel  that  it  would  be 
difficult  to  detect  any  convergence.  But  if  we  take  a  mass  sev- 
eral miles  in  extent,  then  the  lines  will  be  perceptibly  diverg- 
ent. If  now  we  could  substitute  one  force  for  all  these  parallel 
forces  acting  on  one  mass,  a  line  passing  through  that  force  to  the 
center  would  be  the  resultant  of  all  the  lines  of  force.  If,  there- 
fore, a  body  were  supported  on  a  point  any  where  on  that  line, 
its  tendency  to  fall  would  be  exactly  counteracted,  and  it  would 
remain  at  rest,  or  would  be  in  equilibrium,  because  it  would  be 
acted  on  by  equal  and  parallel  forces  in  exactly  opposite  directions. 

How  does  the  force  of  gravity  act  upon  the  atoms  of  a  mass  ?  When 
will  a  body  remain  at  rest? 


68 


NATURAL    PHILOSOPHY. 


To  render  this  evident,  let  the  line  d  b,  Fig.  33, 
be  the  resultant  of  all  the  forces  in  the  mass.  If 
any  portion  of  this  line  were  supported,  the  body 
could  not  fall,  but  the  stability  of  its  support  would 
depend  upon  a  very  important  circumstance. 

1.  If  d  b  were  a  rod,  and  the  point  b  were 
supported,  it  is  evident  that,  as  all  the  mass  is 
above  b,  a  very  slight  motion  of  the  body  would 

cause  some  other  line  to  be  the  resultant,  as  a  c,  and  the  body 
would  fall.     This  is  called  unstable  equilibrium. 

2.  But  if  the  body  were  supported  by  the  point  d,  the  matter 
all  being  below  the  point  of  suspension,  it  is  evident  that  it  could 
not  fall  without  an  entire  revolution  of  the  body.     This  is  called 
stable  equilibrium. 

3.  If  the  body  were  sustained  by  a  point  which  is  at  the  cen 
ter  of  its  mass  of  atoms,  as  at  c,  it  could  remain  at  rest  in  what- 
ever position  it  was  placed,  and  such  a  state  is  called 

Indifferent  equilibrium;  and  the  point  which  thus  sustains 
all  the  parts  in  equilibrio  is  called  the 

Center  of  gravity,  and  also  the  center  of  inertia,  which  may 
be  denned  to  be  that  point  in  any  body  which,  if  supported,  the 
whole  body  will  remain  at  rest,  whatever  position  it  may  occupy. 

Every  solid  body  must  have  such  a  center,  and,  if  that  is  sup- 
ported, the  whole  mass  will  be,  and  if  that  moves,  the  whole 
mass  will  move. 

For  example,  if  two  atoms,  a  b,  Fig.  Fig.  34. 

34,  on  the  end  of  an  inflexible  rod,  have 
their  center  of  gravity  at  c,  and  that  point 
be  supported,  they  will  remain  at  rest. 
If  any  force  is  applied  to  the  point  c,  the  a 
two  atoms  will  move  in  the  same  manner 
that  they  would  if  the  force  were  applied  directly  to  each.  If 
the  support  is  placed  in  any  other  part  of  the  line  out  of  this 
center,  the  equilibrium  will  be  destroyed,  and  one  or  both  will 
fall. 


Describe  unstable,  stable,  and  indifferent  equilibrium.  What  is  meant 
by  the  center  of  gravity  ?  If  the  center  of  gravity  is  supported,  in  what 
condition  will  a  body  be  ? 


CENTER    OF    GRAVITY. 


69 


If  there  are  four  atoms,  a  b  and  af  b', 
Fig.  35,  and  the  center  of  gravity,  c,  be 
supported,  they  will  all  be  in  equilibrium ; 
hence  any  number  of  atoms  have  their  cen- 
ter of  gravity,  which  being  supported,  the 
whole  mass  will  be  at  rest,  or  if  moved,  the 
whole  will  move. 

It  becomes  now  an  important  problem  to 
determine  where  this  center  is  in  any  body 
we  may  have  to  examine. 

1 .  If  the  body  is  a  sphere,  a  regular  prism,  or  a  cylinder,  and 
of  uniform  density,  the  center  of  gravity  will  evidently  be  at  the 
center  of  its  magnitude,  or  geometrical  center. 

2.  If  the  body  be  a  disc  of  uniform  density,  the  centers  of  mag 
mtude,  of  motion,  and  of  gravity  will  exactly  coincide ;  but  if  one 

Fig.  36.  side  of  the  disc  is  thicker,  or  loaded  with  lead, 

then  its  center  of  gravity  will  not  coincide 
with  either  the  center  of  magnitude  or  of 
motion. 

The  apparatus,  Fig.  36,  is  well  fitted  to 
illustrate  these  facts.  The  disc  is  loaded 
with  a  piece  of  lead,  d,  and  pierced  through 
the  center  of  magnitude  and  of  gravity,  a  c, 
so  that  it  can  be  revolved  upon  an  axis.  It 
may  be  used,  also,  to  illustrate  stable  and 
indifferent  equilibrium. 

3.  If  the  body  is  in  the  form  of  a  triangle, 
the  center  of  gravity  is  found  by  bisecting 
two  sides  by  lines  drawn  from  the  op- 
posite angles.  Thus,  let  a.b  c,  Fig.  37, 
be  a  triangle.  Bisect  the  side  a  c  by  b 
n,  and  b  c  by  a  m;  the  center  of  grav- 
ity will  be  at  g,  which  is  found  to  be 
one  third  of  m  a. 

For,  join  n  m ;  then  c  n  m  and  cab  are  sim- 
ilar ;  therefore  c  n  :  c  a : :  n  m  :  a  b  ;  but  c  n  is 
half  of  a  c,  therefore  m  n  is  half  of  a  b. 

Again,  the  triangles  n  g  m  and  gab  are  sim- 


How  is  the  center  of  gravity  determined  in  a  sphere,  prism,  and  cylin- 
der? How  in  a  disc  ?  How  is  the  center  of  gravity  in  a  triangle  determ- 
ined ? 


70  NATURAL    PHILOSOPHY. 

ilar,  and  g  m:  g  a'.'.m  n:  a  b.     m  n  is  half  of  a  b,  and  hence  m  g  is  half  of 
g  a.     The  point  g  is  therefore  one  third  the  distance  from  m  to  a. 

Now,  as  the  center  of  gravity  must  be  in  the  line  m  a,  since  every  line 
drawn  parallel  to  b  c  would  be  bisected,  and  the  center  of  gravity  of  aline 
is  the  center  of  the  line,  and  as  it  must  also  be  in  the  line  b  n,  for  a  similar 
reason  it  must  be  at  their  point  of  intersection,  g. 

Practically,  the  center  of  gravity  may  be  determined  by  sus- 
pending the  triangle  from  the  two  corners  b  and  «,  and  letting 
fall  a  plumb  line  from  each,  as  a  m,  b  n.  Where  the  lines  cross 
at  g  will  be  the  center  of  gravity. 

4.  The  center  of  gravity  in  a  regular  polygon  may  be  found 
by  dividing  it  into  triangles,  arid  then  finding  the  centers  of  the 
several  triangles. 

5.  In  a  regular  pyramid  or  cone,  the  center  of  gravity  is  at  a  point 
one  fourth  of  the  distance  from  the  center  of  their  bases  to  the  apex 

6.  If  bodies  have  irregular  shapes,  their  center  of  gravity  may 
be  found  by  suspending  them  from  two  corners,  as  in  Fig.  33. 

Thus,  suspend  Fig.  33  from  the  point  d,  with  a  plumb  lin* 
passing  in  the  direction  d  b,  and  then  from  the  point  e.  The  in- 
tersection of  the  two  lines  at  c  will  be  the  center  of  gravity,  foi 
this  center  must  be  in  the  line  b  d,  and  also  in  ef;  it  must  be, 
therefore,  at  the  point  where  these  lines  cross  each  other  at  c. 

Stability  of  Bodies. — We  have  seen  that  when  the  center  of 
gravity  is  supported,  the  body  will  be  at  rest.  But  its  stability 
will  depend  upon  thtj  fact  whether  it  is  in  a  state  of  stable,  un- 
stable, or  indifferent  equilibrium. 

1 .  A  solid  body  is  supported  ivhenever  a  plumb  line  from 
the   center   of  gravity  falls   within   its   base. 
Thus, 

Let  A  B,  Fig.  38,  represent  the  leaning  tower 
of  Pisa.  When  the  top,  B,  is  taken  off,  the  cen- 
ter of  gravity  is  at  C,  and  the  line  from  C  fall- 
ing within  the  base,  the  tower  will  be  sustained ; 
but  by  inserting  the  top,  B,  the  center  of  gravity 
is  raised  to  E  ;  and  as  the  line  falls  without  the 
base,  the  tower  will  fall. 

Where  is  the  center  of  gravity  in  a  pyramid  and  cone  ?  How  can  the 
center  of  gravity  be  determined  in  an  irregular  figure  ?  What  rule  for  de- 
termining when  any  body  will  be  supported  ? 


STABILITY    OF    BODIES. 


71 


d 


A  sphere,  d,  Fig.  39,  on  an  inclined 
B  plane,  A  B,  will  roll  down  simply  be- 
cause the  center  of  gravity  is  not  sup- 
ported, while  the  square  body,  g,  will 
remain  at  rest,  or  only  slide  down  the 
plane,  because  the  line  of  the  center  of 
C  gravity  falls  within  the  base. 
2.  The  broader  the  base  is,  and  the  lower  the  center  of  grav 
tty,  the  firmer  will  the  body  stand  ;  and,  on  the  contrary,  as  the 
base  is  made  more  narrow,  and  the  center  of  gravity  raised,  the 
body  becomes  more  and  more  unstable. 

Thus  broad,  low  bodies,  as  houses,  are  upset  with  much  greater 
difficulty  than  those  that  are  high,  with  narrow  bases.  Quad- 
rupeds stand  much  more  firmly  than  birds  and  other  bipeds. 

A  person  carrying  a  weight  on  his  back  must  lean  forward  in 
order  to  bring  the  line  of  the  center  of  gravity  within  his  base. 
If  he  carry  the  weight  in  one  hand,  he  must  lean  in  the  opposite 
direction  for  the  same  reason.  He  will,  therefore,  carry  a  greater 
burden  if  it  be  suspended  on  both  sides  of  his  body. 

The  wonderful  feats  of  rope-dancers,  tumblers,  &c.,  depend 
mainly  on  their  power  of  keeping  their  bodies  in  such  positions  as 
to  cause  the  line  of  the  common  center  of  gravity  always  to  pass 
through  the  point  on  which  they  support  themselves. 

Carriages  and  loaded  teams, 
Fig.  40,  are  sometimes  upset,  be- 
cause the  direction  of  the  center  of 
gravity  falls  without  the  base. 

The  danger  of  upsetting  is  in- 
creased if  the  vehicle  is  in  rapid 
motion  and  the  road  curved,  for 

61  p«  in  this  case  inertia  will  aid  in 

throwing  the  center  beyond  the  base. 

In  such  cases  the  danger  may  be  avoided  by  lying  down  in  the 
carriage,  so  as  to  lower  the  center  of  gravity. 

A  beautiful  illustration  of  stable  equilibrium  is  found  in  a  little 

What  influence  has  the  size  of  the  base  upon  the  stability  of  bodies  ? 
Why  are  carriages  upset  ?  What  can  be  done  to  prevent  a  carriage  from 
upsetting  1  What  illustration  of  stable  equilibrium  ? 


Fig.  40. 


72  NATURAL    PHILOSOPHY. 

toy,  in  which  a  trooper  is  made  to  stand  without  any  apparent 
support. 

In  case  a  tody  is  suspended,  as  a  pendulum,  or  the  beam  of  a 
pair  of  scales,  it  is  necessary  that  the  point  of  suspension  should 
be  a  very  little  above  the  center  of  gravity,  in  order  to  make  a 
stable  equilibrium.  If  it  be  suspended  at  the  center  of  gravity, 
the  equilibrium  will  be  indifferent,  and  if  it  is  below,  the  equi- 
librium will  be  unstable. 

III.  Central  Forces. — Under  the  action  of  gravity  and  any 
projectile  force  which  is  not  in  the  direction  of  the  center  of  the 
earth,  the  motion  described  by  any  body  is  curvilinear. 

1 .  Thus,  suppose  a  body  to  move  under  the  influence  of  a  pro- 
jectile force,  A,  Fig.  41,  which  in  four  Fig  41 
seconds,  moving  with  uniform  velocity, 
would  describe  the  line  A  B.  Now  if, 
under  the  influence  of  gravity,  it  would 
fall  from  B  to  C  in  the  same  time,  then 
in  four  seconds  it  would  describe  the  curve 
Afhk  C,  or  the  force  of  gravity  acting 
constantly  will  cause  it  to  move  through 
spaces  which  will  be  as  the  squares  of  the  times.  That  is,  if  the 
times  A  e,  e  g,  g  i,  i  B,  are  equal,  the  lines  ef,  g  h,  i  k,  B  C 
will  be  as  the  squares  of  these  distances.  The  body,  therefore, 
under  the  influence  of  both  forces,  will  describe  the  curve  of  a 
parabola,*  if  the  force  of  gravity  is  assumed  to  act  parallel  to  it- 
self;  but  as  it,  in  fact,  never  does,  the  curve  is  an  ellipse. 

These  figures,  however,  are  not  described  unless  the  body  move 
in  a  vacuum  ;  for  the  resistance  of  the  air  is  such  that  the  tend- 
ency is  to  uniform  motion,  and  the  curve  actually  described  is 
what  is  called  the 

Balistic  Curve. — That  is,  in  all  cases  where  bodies,  as  cannon 
balls,  are  fired  through  the  atmosphere,  the  air  becomes  com- 
pressed before  them,  so  as  to  alter  their  course  to  the  right  or 
left;  and  if  their  velocity  be  above  1280  feet  per  second,  the 

*  A  parabola  is  one  of  the  sections  of  a  cone.  It  is  a  curve,  any  point 
of  which  is  equally  distant  from  a  fixed  point  and  a  given  straight  line. 

How  should  a  balance  be  suspended?  How  is  curvilinear  motion  pro- 
duced? Illustrate  by  the  diagram.  What  kind  of  a  curve  does  a  body 
describe  under  the  influence  of  a  projectile  force  and  gravity  7 


PROJECTILES GUNNERY.  73 

rate  at  which  air  flows  into  a  vacuum,  it  is  soon  reduced  below 
that  rate. 

2.  Projectiles,  Gunnery. — Bodies  thrown  into  the  air  by  any 
force  are  called  projectiles.     Such  bodies  are  under  the  influence 
of  three  forces,  the  force  of  projection,  the  resistance  of  the  air,  and 
gravity.     A  knowledge  of  the  laws  of  projectiles  is  applied  to  the 
Art  of  Gunnery. 

The  force  (which  is  gunpowder)  is  measured  by  the  motion 
which  a  b511  of  a  given  weight  will  give  to  a  block  of  wood,  sus- 
.  42.  perided  as  A,  Fig.  42,  and  called 

the  Holistic  Pendulum.  When  the 
ball  is  fired  into  the  center  of  per- 
cussion, the  ball  and  block  move  over 
the  graduated  arc  with  a  velocity  as 
much  less  than  the  ball,  as  the  ball 
and  pendulum  together  is  greater. 
By  ascertaining  the  weight  of  the 
ball  and  of  the  block,  and  then  the 
velocity  of  both  over  the  graduated  arc,  it  is  easy  to  determine 
the  velocity  of  the  ball ;  for  the  weight  of  the  ball  will  be  to  that 
of  the  block,  as  the  velocity  of  the  block  is  to  that  of  the  ball. 
By  this  instrument  the  strength  of  powder,  and  the  influence  of 
a  large  or  small  charge,  may  be  determined. 

Gunpowder  expands  5000  feet  per  second,  which  will  commu- 
nicate a  velocity  of  2000  feet  per  second  ;  but,  owing  to  the  re- 
sistance of  the  air,  it  is  soon  reduced  below  1200  feet  per  second  ; 
hence  there  is  little  advantage  in  using  a  large  charge  of  powder. 
The  random  of  a  projectile  is  the  distance  it  reaches  in  a  hori- 
zontal line  before  it  strikes  the  earth.  An  angle  of  45°  gives 
the  greatest  random,  and  for  the  same  number  of  degrees  above 
or  below  45°  the  random  is  the  same. 

3.  If  a  body  be  projected  in  the  direction  of  a  tangent  to  the 
earth's  surface,  the  direction  of  the  force  of  gravity  being  toward 


What  is  a  projectile  ?  To  what  art  are  the  laws  of  projectiles  applied  ? 
How  is  the  velocity  of  a  cannon  ball  measured  ?  What  is  its  expansive 
force  ?  Greatest  velocity  of  a  cannon  ball  ?  What  figure  will  a  body  de- 
scribe if  it  be  projected  in  the  direction  of  a  tangent  to  the  earth's  surface  ? 


74 


NATURAL    PHILOSOPHY. 


its  center,  we  can  easily  determine  the  course  of  the  moving 
body.     Thus, 

Let  C,  Fig.  43,  be  the  center  of  the  earth, 
and  a  body,  as  at  a,  acting  under  the  influ- 
ence of  the  projectile  force  a  ft,  which  in  one 
second  of  time,  moving  with  uniform  velocity, 
would  describe  the  line  a  b.  If,  under  the  in- 
fluence of  gravity,  it  would  fall  from  a  to  d, 
then  in  one  second  it  will  describe  the  diago- 
nal a  f.  Then,  if  the  centrifugal  force  at  f 
would  carry  it  to  g  during  the  second  instant, 
and  the  force  of  gravity  to  h,  it  will  describe 
the  line/&;  and  so  the  third  second  it  will 
be  found  at  n.  But  as  gravity  is  a  constant 
force,  it  will  actually  describe  the  curve  afk  n. 

If  the  projectile  and  central  forces  are  equal, 
the  body  will  describe  a  circle  ;  but  if  the  force 
of  projection,  which  becomes  the  centrifugal  force,  diminishes  at 
different  points  of  its  orbit  as  the  square  of  its  distance  from  the 
center  of  attraction  increases,  then  it  will  be  an  ellipse. 

All  the  planetary  bodies  revolve  in  ellipses,  moving  under  the 
influence  of  the  centripetal  force,  which  is  gravity,  and  the  cen- 
trifugal force,  which  is  the  force  by  which  they  were  first  sent 
forth  into  space.  As  the  planets  are  at  different  distances  from 
the  sun,  and  revolve  with  different  degrees  of  velocity,  their  mo- 
tions are  found  to  conform  to  the  laws  of  bodies  revolving  under 
the  influence  of  two  such  forces  as  gravity  and  the  force  of  pro- 
jection. 

These  laws  may  be  illustrated  and  proved  with  the  apparatus, 
Fig.  44,  which  has  attached  to  it  several  bodies  of  different 
shapes,  as  a  double  cone,  a  chain,  spheroid,  &c.  It  is  found  that 
all  bodies,  when  rapidly  revolved,  will  assume  that  axis  which 
represents  their  shorter  diameter ;  the  shorter  diameter,  there- 
fore, becomes  the  permanent  axis. 

It  is  found  by  experiment, 

1.    That  the  centrifugal  force  is  proportioned  to  the  quantity 

By  what  circumstance  is  the  nature  of  the  curve  determined  ?  What 
curves  do  the  heavenly  bodies  desciibe  ?  Which  is  the  permanent  axis  of 
a  revolving  body  ?  What  is  the  centrifugal  force  proportioned  to  ? 


CENTRAL    FORCES. 


75 


of  matter.     That  is,  as  the  quantity  of  matter  increases,  the  force 
increases. 

2.  This  force  is  proportioned  to  the  distance  of  the  body  from 
the  center  of  motion.     At  twice  the  distance,  the  body  must  be 
forced  toward  the  center  twice  as  far  at  every  revolution. 

3.  If  the  velocity  is  doubled,  then  the  centrifugal  force  is  four 
times  as  great  ;  for  double  the  velocity  gives  double  the  power 
to  fly  off,  and  also  requires  the  body  to  be  moved  toward  the  cen- 
ter with  twice  the  velocity,  which  makes  its  force  four  times  as 
great.     Hence  the  reason  why  large  mill-stones  are  sometimes 
separated  by  a  very  rapid  revolution,   and  why  a  carriage  in 
rapid  motion,  when  turning  the  corner  of  a  street,  is  upset  ;  why, 
in  the  circus,  the  rider  inclines  his  body  within  the  ring,  to  coun- 
teract the  constant  tendency  to  be  thrown  off  in  a  tangent  to  the 
circle  in  which  he  is  moving.     Hence,  in  consequence  of  the  fact 
that  the  centrifugal  forces  of  bodies  revolving  in  the  same  circles 
are  as  the  squares  of  the  velocities,  when  the  velocity  is  very 
great  this  force  may  become  so  great  as  to  cause  the  body  to 
break  away  from  the  central  force.     Thus,  the  velocity  of  the 
earth  might  be  so  increased  as  to  change  the  form  of  its  orbit 
from  an  ellipse  to  a  parabola,  in  which  case  it  would  never  return 
again  to  the  central  power,  the  sun. 

4.  But  when  bodies  revolve  in  dif 
ferent  circles  in  the  same  time,  the 
centrifugal  forces  generated  will  be 
as  their  distances  from  the  centers  of 
motion,  or  as  the  radii  of  the  circles. 
At  twice  the  distance  from  the  cen- 
ter, the  body  must  be  forced  inward 
twice  as  far  at  each  revolution,  and, 
of  course,  its  force  must  be  twice  as 
great.  This  principle  may  be  illus- 
trated by  an  apparatus,  Fig.  44,  in  which  several  bodies,  capable 
of  altering  their  figure,  are  rapidly  whirled  about.  The  matter 

What  effect  has  it  to  double  the  velocity  of  the  revolving  body  ?  What 
other  illustrations  of  centrifugal  force?  What  would  be  the  effect  of  in- 
creasing the  velocity  of  the  earth  in  its  orbit?  What  is  the  law  when 
bodies  are  placed  at  different  distances  from  the  center  of  revolution  ? 


Fig.  44. 


76  NATURAL    PHILOSOPHY. 

tends  to  move  as  far  as  possible  from  the  axis  of  revolution.  If 
our  earth  were  at  first  in  a  plastic  state,  it  would  tend  to  bulge 
out  at  the  equator,  and  become  compressed  at  the  poles  ;  for  the 
velocity  at  the  equator  would  cause  the  matter  to  accumulate 
there.  This  is  the  shape  which  it  actually  has.  The  same 
principle  is  illustrated  in  the  case  of  the  rings  of  Saturn,  and  in 
the  shape  of  all  the  bodies  of  the  solar  system.  The  clay  in  a 
potter's  wheel  also  bulges  out  to  form  bottles  and  other  vessels  as 
the  wheel  rapidly  revolves.  It  will  be  seen  that  the  effect  of 
centrifugal  force  is  to  destroy  either  wholly  or  in  part  the  weight 
of  bodies. 

Thus  any  body  at  the  equator  will  weigh  less,  on  account  of 
its  greater  velocity,  than  at  the  poles,  being  diminished  ¥|¥th  of 
its  weight.  If,  therefore,  the  velocity  at  the  equator  were  seven- 
teen times  as  great  as  at  present,  all  loose  bodies  would  be  thrown 
off,  and  revolve  about  the  earth.* 

IV.  Collision  of  Bodies. — We  have  noticed  that  certain  mod- 
ifications of  the  cohesive  force  gave  rise  to  the  property  of  elas- 
ticity, a  power  which  some  bodies  have,  when  compressed,  of  re- 
storing themselves  to  their  former  position ;  but  this  property  is 
possessed  in  different  degrees,  and  in  some  bodies  it  is  wholly 
wanting. 

Thus  ivory,  glass,  India  rubber,  wool,  &c.,  are  very  elastic; 
lead,  clay,  and  wax  are  non-elastic  bodies.  These  properties  give 
rise  to  different  effects  in  the  two  classes  when  they  impinge  or 
strike  against  each  other. 

1 .  When  inelastic  bodies  impinge  upon  each  other,  there  is  no 
rebound ;  but  if  both  bodies  are  moving  in  the  same  direction, 
they  will  move  on  together  after  impact  with  a  velocity  corre- 
sponding to  their  quantities  of  matter  and  the  sum  of  their  veloc- 
ities before  impact,  or  their  velocities  will  equal  their  momenta 
divided  by  their  quantity  of  matter. 

*  The  weight  of  a  body  is  diminished  as  we  go  from  the  pole  to  the 
equator  in  the  ratio  of  the  square  of  the  cosine  of  latitude. 

What  shape  wouttl  the  earth  assume  if  it  were  first  created  in  a  plastic 
state?  What  other  illustrations  in  nature?  What  is  the  effect  of  centrifu 
gal  force  upon  the  weight  of  bodies  ?  When  inelastic  bodies  impinge  upon 
each  other,  what  is  the  law  of  motion  ? 


COLLISION    OF    BODIES.  77 

If  two  bodies  are  moving  in  opposite  directions,  their  velocity 
after  impact  will  equal  the  difference  of  their  momenta  divided 
by  their  quantity  of  matter. 

For  it  has  already  been  shown,  that  the  velocity  of  any  moving 
body  may  be  found  by  dividing  the  momentum  by  the  quantity  of 
matter  ;  and  hence  the  velocity  of  any  number  of  moving  bodies 
after  impact  may  be  found  by  dividing  the  sum  or  difference  of  their 
momenta  by  their  quantity  of  matter,  whether  they  are  moving  in 
the  same  or  in  opposite  directions  before  they  come  into  collision. 

These  facts  may  be  illustrated  by  two  lead  or  clay  balls,  Fig. 
22,  p.  51,  which  are  of  exactly  equal  size. 

Exp. — By  raising  a  to  6  and  allowing  it  to  fall  upon  b,  the  two  balls  will 
move  to  3  in  the  same  time  that  a  moved  from  6  to  0. 

PROBLEMS. 

1 .  If  a  lead  ball  weighing  two  pounds,  and  moving  with  a  ve- 
locity of  1200  feet  per  second,  strike  another  ball  of  the  same 
weight  at  rest,  what  will  be  their  velocity  after  impact  ? 

Ans.,  600  feet  per  second. 

2.  If,  in  the  above  problem,  the  second  ball  were  moving  200 
feet  per  second  in  the  same  direction,  what  would  be  their  ve- 
locity after  impact  ? 

Ans.,  700  feet. 

3.  If  the  second  ball  were  moving  200  feet  in  an  opposite  di- 
rection, all  other  conditions  being  the  same  as  in  the  first  prob- 
lem, what  would  be  their  velocity  after  impact  ? 

Ans.,  500  feet. 

4.  If  the  two  balls  were  moving  with  equal  velocities  in  op- 
posite directions,  what  would  be  their  velocity  after  impact  ? 

2.  When  elastic  bodies  come  into  collision,  a  very  remarkable 
law  is  developed,  which  appears  at  first  view  to  be  paradoxi- 
cal ;  viz., 

The  velocity  lost  by  one  and  imparted  to  the  other  is  exactly 
double  that  which  it  would  have  were  the  bodies  inelastic.  This 

How  may  the  velocity  of  any  number  of  moving  bodies  impinging  upon 
each  other  be  determined  ?  What  is  the  law  of  impact  when  elastic  bodies 
impinge  upon  each  other  ? 


78 


NATURAL    PHILOSOPHY. 


law  is  due  to  the  power  the  parts  compressed  have  of  restoring 
themselves. 

Thus,  if  one  ivory  ball  impinge  upon  another,  Fig.  45,  and 
strike  it  with  a  force  equal  to  three,  both  m  45 

balls  will  be  compressed  at  the  point  of 
impact,  and  the  parts,  in  being  restored, 
react  upon  each  other,  and  double  the 
effect,  or  make  the  blow  equal  to  six.  If 
the  balls  are  equal,  the  momentum  of 
one  is  wholly  communicated  to  the  oth-  A 
er,  and  it  moves  after  impact  with  the 
same  velocity  as  the  first  ball,  which  will  r- 

be  stopped.     If  they  move  with  equal        ^!"i|in'|i!i"11""1 'H"'i"'i'i'iniiii"ii."iiMiinii 

velocities  in  opposite  directions,  they  will  rebound,  each  with  the 
same  velocity  with  which  they  met.  This  fact  is  easily  shown 
by  these  balls.  This  is  the  reason  that  a  hard  body,  when  struck, 
causes  a  rebound  to  take  place. 

Exp. — If  the  ball  a  be  let  fall  from  A  upon  b,  its  own  motion  will  be 
stopped,  but  it  will  impart  an  equal  motion  to  c,  and  thence  through  d  to  e. 
As  there  are  no  bodies  beyond  e,  it  will  receive  the  motion,  and  move  to  3. 
If  a  b  be  let  fall  from  3  upon  the  remaining  balls,  d  e  will  move  to  3,  and 
all  the  rest  will  be  stationary.  If  two  balls  are  met  at  0  from  3  3,  they 
will  rebound  with  equal  velocities. 

In  cases  where  elastic  bodies  strike  on  a  hard  surface,  in  the 
rebound,  the  angle  of  incidence  is  always  equal  to  the  angle  of 
reflection. 

Thus,  let  d,  Fig.  46,  strike  on  the  surface  c,  the 
angle  d  c  b  is  equal  to  b  c  a.  The  same  law  holds 
in  respect  to  light  and  heat.  If  the  ball  fall  per- 
pendicularly, it  will  return  by  the  same  path.  _ 

It  appears  from  the  preceding  experiments  with 
the  marble  balls,  that 

When  two  equal  elastic  bodies  impinge  on  each  other,  each 
ynoves  after  impact  with  the  velocity  which  the  other  body  had 
before  impact.  Thus,  when  b  and  a  meet  with  equal  velocities, 
they  rebound  with  equal  velocities  ;  when  d  falls  upon  c  at  rest,  c 
moves  with  the  velocity  of  d,  and  d  with  that  of  c  ;  that  is,  d  re- 
mains at  rest. 

If  the  balls  are  not  all  of  the  same  weight,  then  the  velocity 

Explain  this  law.  Illustrate  the  laws  of  impact  with  the  ivory  balls. 
What  is  the  angle  of  incidence  and  of  reflection  ?  How  do  they  compare 
with  each  other  ? 


COLLISION    OF   BODIES.  79 

of  the  larger  ball,  if  at  rest  when  struck,  will  be  as  much  less 
than  that  of  the  smaller  as  its  quantity  of  matter  is  greater,  while 
the  velocity  of  the  smaller  ball,  under  the  same  conditions,  will 
be  as  much  greater  than  that  of  the  larger  as  its  quantity  of 
matter  is  less. 

If  there  are  a  succession  of  balls  of  equal  weights,  and  one  of 
the  balls,  as  e,  Fig.  45,  be  let  fall  against  the  others,  they  will 
all  remain  at  rest  except  a,  and  that  will  move  with  the  velocity 
of  e.  If  two  balls,  a  b,  be  let  fall  upon  the  remaining  three,  they 
will  impart  their  velocity  to  the  two  on  the  other  side  of  c. 

These  laws  may  be  rendered  familiar  by  a  few  problems  : 

1 .  If  a  marble  ball  weighing  two  pounds,  and  moving  ten  feet 
per  second,  strike  another  ball  of  the  same  weight  at  rest,  what 
will  be  the  velocity  of  each  ball  after  impact  ? 

2.  If  the  two  balls  in  the  above  problem  are  each  moving 
ten  feet  per  second,  but  in  exactly  opposite  directions,  what  will 
be  their  velocity  then  after  impact  ? 

Ans.,  10  feet  per  second. 

3 .  If  the  two  balls,  A  B,  as  above,  are  each  moving  in  the  same 
direction,  the  first  20,  and  the  second  200  feet  per  second,  what 
will  be  the  velocity  of  each  after  impact  ? 

Ans.,  A  —  200  feet,  B  =  20  feet. 

4.  The  ball  A,  weighing  ten  pounds,  and  moving  with  a  ve- 
locity of  twenty  feet  per  second,  impinges  on  the  ball  B,  which 
weighs  five  pounds,  and  is  at  rest.     What  are  the  velocities  of 
A  and  B  after  impact  ? 

Ans.,  Velocity  of  A  =  10  feet,  B  =  20  feet  per  second. 

5.  If  both  balls  are  in  motion  in  the  same  direction,  A  twenty 
feet,  and  B  ten  feet  per  second,  what  velocity  will  each  have 
after  impact  ? 

Ans.,  A=10  feet,  B=30  feet. 

6.  If  both  balls  move  in  opposite  directions,  the  velocity  and 
weight  being  as  in  problem  5,  what  would  be  their  velocities  after 
impact  ? 


80  NATURAL    PHILOSOPHY. 


CHAPTER  III. 

OF  THE  MECHANICAL  POWERS. 

FOR  the  purpose  of  transmitting  force  and  motion,  certain  ma- 
chines have  been  invented,  called 

The  Mechanical  Powers,  the  object  of  which  is  to  change 
the  direction  of  motion,  to  increase  force  at  the  expense  of  ve- 
locity, or  velocity  at  the  sacrifice  of  force.  All  machines,  what- 
ever their  form,  may  be  reduced  to  six  : 


1.  The  Lever. 

2.  The  Wheel  and  Axle. 

3.  The  Pulley. 


4.  The  Inclined  Plane 

5.  The  Screw. 

6.  The  Wedge. 


These  may  be  further  reduced  to  two  elementary  principles, 
for  the  wheel  and  axle,  and  the  pulley,  act  on  the  same  principle 
as  the  lever,  while  the  wedge  and  screw  are  inclined  planes. 

By  the  term  weight  is  meant  any  resistance  to  be  overcome, 
and  by  power,  the  force  which  overcomes  it.  They  are  repre- 
sented by  P  and  W. 

There  is  one  law  which  applies  to  all  machines,  whatever 
their  form  or  structure.  It  is  called  the  law  of  Virtual  Velocities. 

This  law  is,  that  the  power  and  weight  will  be  in  equilibrium 
when 

The  product  of  the  weight  into  the  vertical  space  which  it 
passes  through  is  equal  to  the  prod- 
uct  of  the  power  into  the  vertical 
space  it  passes  through  ;  and  if  this 
relation  is  disturbed,  motion  will 
ensue. 

Thus,  in  Fig.  47,  let  P  W  re- 
volve on/;  then  P  :  W  :  :  c  d  :  a  b. 
=  Wxcd.     When  motion 


What  is  the  object  of  machines?  Mention  the  several  mechanical 
powers.  To  how  many  simple  principles  may  they  be  reduced  ?  Meaning 
of  weight  and  power.  What  law  applies  to  all  machines  1 


MECHANICAL    POWERS.  81 

takes  place,  the  velocity  of  the  weight  into  the  weight  equals  the 
velocity  of  the  power  into  the  power. 

In  estimating  the  force  of  any  of  the  mechanical  powers,  we 
must  first  determine  in  each  one  the  Law  of  Equilibrium,  that 
is,  the  conditions  which  must  be  observed  that  the  power  and 
weight  may  exactly  balance  each  other ;  and  in  ascertaining 
what  these  laws  are,  no  notice  is  taken  of  any  impediments  to 
motion  arising  from  friction  or  any  other  cause.  The  laws  are 
first  determined  theoretically,  and  allowance  made  afterward, 
as  there  always  must  be  in  practical  mechanics,  for  any  disturb- 
ing causes. 

SECTION  L— OF  THE  LEVER,  THE  WHEEL  AND  AXLE,  AND  THE  PULLEY. 

As  it  is  the  object  in  all  the  mechanical  powers  first  to  ascer- 
tain the  laws  of  equilibrium  between  the  power  and  the  weight, 
it  is  found 

I.  In  the  lever  that  equilibi'ium  will  be  maintained  when  the 
pi'oduct  of  the  poiver  into  its  distance  from  the  fulcrum  is  equal 
to  the  product  of  the  weight  into  its  distance  from  the  same  point. 

II.  In  the  wheel  and  axle,  the  poiver  and  weight  will  balance 
each  other  when  the  power  multiplied  into  the  radius  of  the 
wheel  is  equal  to  the  weight  multiplied  into  the  radius  of  the 
axle ;  and  in  itie  wheel  and  pinion,  the  product  of  the  power 
into  the  number  of  teeth  in  the  wheel  is  equal  to  the  product  of 
the  weight  into  the  number  of  notches  or  leaves  in  the  pinion. 

III.  In  the  pulley,  equilibrium  will  be  maintained  when  the 
power  multiplied  into  twice  the  number  of  movable  pulleys  is 
equal  to  the  weight;  and  in  case  each  movable  pulley  has  a  sep- 
arate string,  we  may  ascertain  the  weight  by  raising  2  to  a 
power  equal  to  the  number  of  movable  pulleys,  and  multiply- 
ing it  by  the  power.     In  all  the  above  cases,  if  a  slight  force  be 
added  to  the  power,  the  weight  will  be  raised.     But  there  is  no 
advantage  gained,  for  wlutt  is  gained  in  power  is  lost  in  time^ 
or  the  poiver  must  move  as  much  faster  tfian  the  weight  as  its 
quantity  of  matter  is  less. 

What  is  the  first  object  in  investigating  the  action,  of  the  mechanical 
powers  ? 

D  2 


82 

I.  Lever. — A  lever  is  an  inflexible  rod,  of  uniform  magnitude, 
capable  of  moving  freely  around  some  point  as  a  center  of  mo- 
tion, called  ihefidcrum. 

Law  of  Equilibrium  in  the  Lever. — In  the  lever,  the  weight 
and  power  will  be  in  equilibrium,  when  they  are  to  each  other 
inversely  as  their  distances  from  the  fulcrum;  or  when  the  prod- 
uct of  the  weight  into  its  distance  from  the  fulcrum  is  equal  to 
the  product  of  the  power  into  its  distance  from  the  same  point. 

Thus,  let  A  B,  Fig.  48,  be  a  lever,  and  F  the  fulcrum,  the 
power  and  weight  will  be  in  Fig.  48. 

equilibrium  when  P  :  W  :  :  B     4  r— ^ — 2     1     A    i     3     3 
F  :  A  F  ;   for  if  the  power   p  ^          £          I? 
and  weight  are  at  equal  dis-         ^0  10 

tances  from  F,  the  power  will  equal  the  weight,  and  they  will 
remain  at  rest ;  for  W(10)  into  B  F(4)  is  just  equal  to  P(10)  into 
A  F(4)  =  40. 

But  if  the  fulcrum  were  placed  at  2  toward  W,  then,  as  the 
long  arm  would  be  three  times  the  length  of  the  short  arm,  one 
pound  at  P  would  sustain  three  at  W,  or  ten  pounds  would  sus- 
tain thirty ;  if  the  long  arm  be  four  times  the  short  arm,  then 
the  power  will  sustain  four  times  its  weight.  On  the  other  hand, 
if  the  fulcrum  be  placed  near  P,  the  power  must  be  proportion- 
ably  increased  to  sustain  the  weight. 

Levers  are  of  three  kinds.  In  the  first,  the  fulcrum  is  between 
the  power  and  the  weight.  In  the  second,  the  weight  is  between 
the  fulcrum  and  the  power ;  and  In  the  third,  the  power  is  be- 
tween the  fulcrum  and  the  weight. 

1 .  In  the  first  kind  of  lever,  the  fulcrum  is  between  the  power 
and  the  weight. 

Thus,  as  in  the  common  crow-  Fig.  ^9. 

bar,  let  A  B,  Fig.  49,  be  a  lever, 


and  F  the  fulcrum  ;  then  I    *«»***  i 

The  power  and  weight  will  be  in  p  A 

equilibrium  when  the  product  ofPll  f§  w 

multiplied  into  A  F  equals  the  prod-     *  d! 
uct  of  W  multiplied  into  FB,  orPxAF  = 


What  is  the  law  of  equilibrium  in  the  lever  1  Illustrate  this  law.  How 
many  kinds  of  levers  are  there  1  How  are  they  distinguished?  What  is 
*,he  law  of  equilibrium  in  a  lever  of  the  first  kind  ? 


THE    LEVER.  83 

Prob.  1.  If  the  weight  is  200  pounds,  the  short  arm  2  feet, 
and  the  long  arm  10  feet,  what  is  the  power  ? 

To  determine  this,  we  have  only  to  apply  the  rule :  Multiply 
the  short  arm  into  the  weight,  and  divide  the  product  by  10,  the 

2  X  200 
long  arm,  and  it  will  equal  the  power.     — — — =40  Ibs. 

2.  If  the  power  is  40  pounds,  the  long  arm  10,  and  the  short 
arm  2,  what  is  the  weight  ?  Multiply  40  by  10,  and  divide  by  2. 

Ans.,  40  x  10-^2=200  Ibs. 

If  the  product  of  the  long  arm  of  the  lever  into  the  power  is 
greater  than  that  of  the  short  arm  into  the  weight,  motion  will 
take  place,  and  the  weight  will  be  lifted. 

But  an  important  circumstance  should  be  noticed  here,  one 
which  pertains  to  most  machines  for  raising  weights.  The  power 
must  move  as  much  further  than  the  weight  as  its  distance  from 
the  fulcrum  is  greater,  and  its  velocity  must  be  increased  in  the 
same  ratio. 

Thus,  if  40  pounds  set  in  motion  200  pounds,  it  must  be  placed 
five  times  as  far  from  the  fulcrum  ;  and,  in  order  to  move  it  one 
foot,  the  power  must  travel  five  feet,  and,  of  course,  its  velocity 
must  be  five  times  as  great ;  hence  what  is  gained  in  power  is 
lost  in  time.  One  man  may  lift  a  weight  which  requires  the 
strength  of  five,  but  then  he  must  pass  over  five  times  the  space, 
and,  of  course,  will  be  five  times  as  long  in  doing  it. 

PROBLEMS. 

1.  What  would  be  the  length  of  the  long  arm  of  a  lever,  placed  undei 
the  earth,  supposing  it  to  weigh  800  trillions  of  tons,  the  fulcrum  being  4000 
miles  from  the  center,  and  the  power  being  a  man  weighing  200  pounds  ? 

Ans.,  32  quintillioos  of  miles. 

2.  How  far  must  he  move  to  raise  the  earth  one  foot? 

Ans.,  8  quadrillions  of  feet. 

3.  How  long  would  he  be  in  accomplishing  the  feat,  if,  in  his  motion,  he 

followed  the  law  of  falling  bodies?     (See  page  66,  T=    /-.) 

4.  What  would  be  his  velocity  the  last  second  of  his  fall  ? 

Arts.,  V=2g-T. 

2.  In  the  second  kind  of  lever,  the  weight  is  between  the 
Is  there  any  advantage  gained  by  the  lever  ? 


84  NATURAL    PHILOSOPHY. 

power  and  the  fulcrum ;   thus,   A  F,  F&- 50- 

Fig.  50,  is  the  lever,  F  the  fulcrum,  W 
the  weight,   and  P  the  power.     The 
same  rule  applies  in  this  case  as  in  the     F  B 
preceding.  /\  I    •   e  3  4  i 


The  product  of  the  weight  into  its  w 
distance  from  the  fulcrum  is  equal  to  the  product  of  the  power 
into  its  distance  from  the  fulcrum  ;  for  example,  let  W  =  200, 
P  =  40,  FB:=2,  and  FA  =  10;  then  200  x  2  =  40  X  10  =  400. 

Prob.  1.  What  power  would  be  sufficient  to  upset  a  building 
weighing  20  tons,  applied  to  the  end  of  a  lever  100  feet  long, 
the  fulcrum  being  1 0  feet  from  the  weight  ? 

Ans.,  2  tons. 

2.  A  man,  by  exerting  a  force  of  250  pounds,  uprooted  a  tree 
with  a  lever  30  feet  long,  the  fulcrum  being  5  feet  from  the  base 
of  the  tree.     What  resistance  did  he  overcome  ? 

Ans.,  1500  Ibs. 

3.  Two  men  carried  a  weight  of  200  pounds  between  them 
on  a  lever  8  feet  in  length ;  the  weight  was  placed  3  feet  from 
the  end  of  the  lever ;  what  portion  of  it  did  each  sustain  ? 

Ans.,  75  Ibs.  and  125  Ibs. 


^^vl*}  p 
' 


3.  In  a  lever  of  the  third  kind,  the  Fig.  5L 

power  is  between  the  weight  and  ful- 
crum  ;  thus,  B  F,  Fig.  51,  is  the  lever, 
F  the  fulcrum,  P  the  power,  and  W 
the  weight.  The  same  rule  may  be  ap- 
plied here  :  PxAP  =  WxFB. 

But  it  will  be  observed,  in  this  case,  that  the  power  must  be 
greater  than  the  weight,  and  there  is  said  to  be  a  mechanical  dis- 
advantage ;  and  yet  what  is  lost  in  power  is  gained  in  time. 
For  example,  if  A  F  is  but  half  of  F  B,  the  power  must  be 
double  that  of  the  weight  ;  but  when  motion  takes  place,  the 
power  moves  but  one  foot  to  raise  the  weight  two  feet. 

In  the  limbs  of  animals  we  have  examples  of  levers  ;  they  are 

Describe  the  third  kind  of  lever.  What  relation  does  the  power  bear 
to  the  weight  ? 


COMPOUND   LEVER.  85 

mostly  of  the  third  kind,  and  the  loss  in  power  has  a  full  com- 
pensation in  the  greater  extent  and  freedom  of  motion. 

Prdb.  A  man  sustained  on  the  ends  of  his  fingers,  in  a  hori- 
zontal position,  a  weight  of  200  pounds  ;  on  the  supposition  that 
his  arm,  from  the  elbow,  was  1  8  inches  in  length,  and  the  power 
applied  2  inches  from  the  fulcrum,  how  much  force  did  he  exert  ? 

Ans.,  1800  Ibs. 

4.  Weight  of  the  Lever.  —  In  determining  the  laws  of  equilib- 
rium in  all  the  above  cases,  the  weight  of  the  lever  has  not  been 
taken  into  the  calculation  ;  but  in  practice,  this  weight  must  be 
considered. 

(1.)  In  a  lever  of  the  first  kind,  if  the  prop  is  in  the  middle, 
the  lever  will  be  sustained  on  its  center  of  gravity,  and  no  allow- 
ance is  required  ;  but  in  any  other  position,  the  weight  of  the 
lever  must  be  determined. 

As  the  whole  weight  of  a  lever  is  at  its  center  of  gravity,  the 
part  for  which  allowance  must  be  made  will  be  equal  to  its 
iveight  multiplied  into  the  distance  of  its  center  of  gravity  from 
the  fulcrum. 

If  we  represent  the  weight  of  the  lever  by  w,  then,  in  a  lever  of  the 

Fig.  53.  first  kind,  Fig.  52,  c  being  its  center  of  gravity, 

A  W         F          B  ^e  distance  of  this  point  from  F  is  equal  to  half 

I  -  -J  -  TT  -  1      of  AB  —  BF  ;  hence  half  of  w,  multiplied  into 

<*         JH  AB  —  BF,  must  be  added  as  a  portion  of  the 

JL     power,  and  then  the  formula  for  the  equilibrium 

Op  -WO    will  bePxAF  +  jw  (AB—  BF)=WxBF. 

(2.)  In  the  second  kind  of  lever,  the  fulcrum  being  at  the  end,  the  dis- 
tance of  the  center  of  gravity  will  be  half  of  A  B.  Hence  the  lever  be- 
comes a  portion  of  the  weight,  and  we  shall  have  the  expression  P  xAB  = 


(3.)  In  the  third  kind  of  lever,  the  weight  of  the  lever  is  a  portion  of 
the  weight  to  be  raised,  and  we  have  the  same  formula  as  in  the  lever  of 
the  second  kind. 

5.  Compound  Lever.  —  The  compound  lever  consists  of  sev- 
eral simple  levers  united  together. 

a  be,  Fig.  53,  represents  three  levers,  so  arranged  that  the  long 
arms  are  all  on  the  side  of  the  fulcrum  with  the  power,  and  the 
short  arms  on  the  side  with  the  weight  ;  hence 

What  effect  has  the  weight  of  the  lever  in  modifying  the  laws  of  equilib- 
rium ?  What  is  the  rule  for  determining  the  allowance  to  be  made  for  the 
weight  of  the  lever  ?  Describe  the  compound  lever. 


86 


NATURAL    PHILOSOPHY. 
Fig.  53. 


24  CF 

1    2    3    4     5     \6 
7i              f      8Q* 

m     a                 .dl  !  L 

«      i      «      t              (7 

A~ 

16 

6 

J 

32 

/\ 

^X1 

T%e  power  and  weight  will  be  in  equilibrium  when  the  prod- 
uct of  all  the  long  arms  into  the  power  equals  that  of  all  the 
short  arms  into  the  weight. 

By  means  of  this  apparatus  the  laws  of  equilibrium  may  be 
proved  experimentally.  Thus, 

Exp. — Suspend  a  32  ounce  weight,  W,  from  the  end  of  a;  the  long 
arm  of  a  is  twice  the  short  arm ;  16  ounces  at  d  will  just  sustain  the  weight 
The  long  arm  of  the  lever  b  is  also  double  its  short  arm,  and  hence  8  ounces 
at  f  will  sustain  the  16  ounces  at  d.  The  long  arm  of  c  is  also  twice  that 
of  the  short  arm,  and  hence  4  ounces  at  P  will  sustain  8  ounces  atf.  To 
sustain  32  ounces  at  W,  then,  will  require  a  force  of  only  4  ounces  at  P. 
If  the  rule  is  applied  in  this  case,  it  will  be  found  that  2X2X2X32  =  4x 
4X4X4  —  256. 

6.  Weighing  Machine. — Large  machines  for  weighing  coal, 
hay,  and  other  heavy  articles,  are  constructed  on  the  principle  of 
the  compound  lever. 

Thus,  let  A  B,  Fig.  54,  be  a  platform,  resting  on  H  I,  on  to 

Fig.  54. 


which  the  load  may  be  drawn.    The  platform,  when  used,  presses 


On  what  principle  does  it  act  ?     On  what  principle  are  weighing 
chines  constructed  ?     Describe  the  cut. 


* 

LEVERS BALANCE.  87 

on  two  levers  of  the  second  kind,  C  P77,  having  their  fulcrums  at 
C  C',  at  the  points  W  W.  DP7  is  also  a  lever  of  the  second 
kind,  receiving  the  weight  at  W.  To  this  lever  there  is  attached 
a  wire,  P7  W,  connected  with  a  lever  of  the  first  kind,  which 
acts  on  the  principle  of  the  steel-yard,  W7  P. 

It  is  easy  to  estimate  the  power  of  this  machine ;  for,  suppose 
the  long  arms  of  the  two  levers,  C  P'7,  are  each  five  times  their 
short  arms,  then  only  two  tenths  of  the  load  will  press  at  P77  upon 
W.  If  the  long  arm  of  the  lever  D  P7  is  also  five  times  the 
short  arm,  then  a  force  equal  to  }th  of  /^ths,  or  -^jth  at  P'  or  W7, 
will  sustain  the  load.  If,  finally,  the  long  arm  of  the  lever  W7  P 
is  five  times  its  short  arm,  then  the  force  at  ?  S  need  be  but 
•,-^3-th  of  the  weight. 

Prob.  1.  On  the  above  supposition,  if  the  load  weigh  5  tons, 
what  power  will  balance  it  at  S  ? 

Ans.,  80  Ibs. 

2.  If  a  25  pound  weight  is  applied  at  S,  what  is  the  weight 
of  the  load  ? 

Ans.,  3125  Ibs. 

7.  Illustrations  of  different  Levers. — (1.)  The  common  steel- 
yard is  a  lever  of  the  first  kind,  in  which  one  arm  is  much  longer 
than  the  other.  The  power  is  applied  to  the  long  arm,  and  is 
made  to  counterbalance  different  weights  attached  to  the  short 
arm,  by  moving  it  to  a  greater  or  less  distance  from  the  fulcrum. 
Handspikes,  crowbars,  &c.,  are  levers  of  the  first  kind. 

(2.)  Balance. — The  common  balance  is  also  a  lever  of  the  first 
F.    K  kind,  in  which  the  two  arms  are  ex- 

actly  equal,  Fig.  55.  The  fulcrum 
is  placed  at  a  very  small  distance 
below  the  center  of  gravity,  and 
weights  are  applied  in  one  scale,  and 
the  substance  weighed  in  the  other. 
The  longer  the  beam  of  the  balance, 
the  more  sensitive  it  becomes.  In 
delicate  balances,  the  fulcrum  is  made 
of  hardened  steel,  or  agate,  in  the  form  of  a  thin  edge,  so  as  to 
avoid  friction,  and  prevent  it  from  wearing  as  the  beam  turns. 
The  beam  should  be  as  light  as  possible,  and  all  the  parts  con- 
nected with  it  should  be  made  in  the  most  accurate  manner. 

Describe  the  common  balance.     On  what  principle  does  it  act  ? 


88  NATURAL    PHILOSOPHY. 

Balances  are  now  constructed  so  accurately  as  to  weigh 
of  a  grain. 

(3.)  The  Bent-lever  Balance,  Fig.  56,  Fig.  56. 

differs  from  the  preceding  in  the  fact 
that  the  weight  is  counterbalanced  by  a 
loaded  index,  C,  which  moves  over  a 
graduated  arc,  G  F. 

In  this  scale  an  equilibrium  will  be 
produced  when  B  K  is  to  B  D  as  C  to 
E,  or  when  the  'product  of  the  short 
arm,  B  K,  multiplied  into  the  iveight, 
equals  the  product  of  the  long  arm,  B 
D,  multiplied  into  the  poiver. 

If  weights  are  placed  in  the  ^cale  E, 
the  index  will  move  toward  G  until  the 
equilibrium  is  restored,  and  the  number 
on  the  graduated  arc  will  indicate  the  number  of  pounds  which 
have  been  added. 

(4.)  The  Crane  is  a  lever  of  the  second  kind,  and  is  much  used 
in  unloading  vessels,  where  heavy  merchandise  is  to  be  moved  a 
short  distance. 

Shears  are  double  levers  ;  so  are  the  jaws  of  animals. 

The  bones  of  animals  are  striking  illustrations  of  levers  of  the 
third  kind.  The  joints  are  the  fulcrums,  the  muscles  the  powers, 
and  the  limbs  or  weights  held  upon  the  ends  of  the  bones  are 
the  weights.  In  this  case  the  mechanical  disadvantage  has  a 
full  compensation,  for  it  is  only  necessary  for  the  muscle  to  con- 
tract slightly  in  order  to  move  the  limb  through  a  large  space ; 
and  this  is  what  is  especially  needed  by  man  in  order  to  give  him 
quickness  of  motion.  By  the  aid  of  his  superior  intelligence,  he  is 
enabled  to  employ  the  various  agents  of  nature  to  supply  him  with 
physical  power. 

II.  Wheel  and  Axle. — 1.  The  wheel  and  axle  is  a  combina- 
tion of  a  series  of  levers  of  the  first  kind.  The  radii  of  the  wheel 
are  the  long  arms,  and  the  radii  of  the  axle  the  short  arms,  while 
the  axis  is  the  fulcrum. 

If,  therefore,  we  can  ascertain  the  diameter  of  the  wheel  and 

Describe  the  bent-lever  balance.  Describe  the  crane.  What  kind  of 
levers  are  the  limbs  of  animals  ?  What  advantage  have  they  ?  Describe 
tne  wheel  and  axle. 


WHEEL    AND    AXLE. 


89 


of  the  axle,  the  law  of  equilibrium  is  easily  determined  :  it  is  the 

same  as  that  of  the  lever. 

Fig.  57.  Thus,  let  a  t>,  Fig.  57, 

be  a  wheel  and  axle,  or  a 
series  of  them  ;  let  the  ra- 
dius of  the  axle  be  one 
inch,  and  the  radii  of  the 
wheels  two,  three,  and  four 
inches .  E  ach  of  the  small- 
er wheels  may  be  used  as 
an  axle  in  reference  to  the 
larger  one. 

By  the  law  of  inverse 
proportion,  the  power  is  to  the  weight  as  the  radius  of  the  axle 
to  the  radius  of  the  wheel,  or 

The  power  and  weight  will  be  in  equilibrium  when  the  power 
multiplied  into  the  radius  of  the  wheel  equals  the  weight  midti- 
plied  into  the  radius  of  the  axle. 

This  rule  may  be  proved  experimentally  thus  : 
Exp. — Suspend  24  ounces,  W,  from  the  axle  b.  As  the  wheel  c  has  twice 
the  radius  of  b,  it  will  require  but  12  ounces  to  balance  the  weight.  The 
wheel  d  is  three  times  b,  and  hence  8  ounces  will  sustain  the  weight ;  a  is 
four  times  b,  and  hence  6  ounces  at  a  will  keep  the  24  ounces  at  b  exactly 
balanced. 

Prob.  1.  A  weight  of  72  pounds  was  suspended  on  the  axle 
at  b.  What  power  will  balance  it  on  the  large  wheel  a  ?  what 
one? 

2.  One  hundred  pounds  applied  to  the  wheel  a  will  sustain 
how  many  pounds  at  b  ?  how  many  at  c  and  d  ? 

3.  If  100  pounds  applied  to  a  keep  in  equilibrium  2000  pounds 
at  b,  what  is  the  relation  of  the  wheel  to  the  axle  ? 

Fig,  58.  2.  The  Capstan,  Fig.  58,  acts  on  the  same  prin- 

ciple as  the  wheel  and  axle.    Instead  of  the  wheel, 
levers  are  used  to  turn  the  axle.     If  it  is  placed 
in  a  horizontal  position,  it  is  called  a  Windlass. 
In  practical  mechanics,  something  must  be  allowed  for  friction 
and  for  the  rigidity  of  the  cordage.    A  slight  force  must  also  be 

What  is  the  law  of  equilibrium  ?  Describe  the  capstan — windlass.  Why 
must  a  slight  force  be  added  to  the  power  in  using  the  wheel  and  axle  ? 


90 


NATURAL    PHILOSOPHY. 


added  to  the  power  to  cause  motion  \o  take  place,  and  the  mo- 
tion will  be  rapid  or  slow  according  to  the  intensity  of  this  addi- 
tional force. 

3.  The  wheel  and  axle  is  a  very  useful  machine,  and,  as  the 
power  depends  upon  the  relation  of  the  radius  of  the  wheel  to 
that  of  the  axle,  if  the  latter  is  diminished  and  the  former  in- 
creased, the  greater,  in  both  cases,  will  the  power  become.  But 
there  is  a  limit  to  this  increase  of  power  ;  the  axle  can  not  be 
diminished  beyond  a  certain  size  without  breaking,  nor  can  the 
wheel  be  enlarged  to  a  very  great  extent  without  becoming  un- 
wieldy. To  obviate  this  and  to  secure  the  requisite  power,  the 
axle  is  made  of  unequal  size. 

Thus,  in  Fig,  59,  the  rope  is 
coiled  around  the  smaller  part  of 
the  axle,  b,  and,  passing  around 
a  pulley,  is  coiled  also  around  the 
larger  diameter  a.  When  the 
wheel  is  turned,  the  rope  un- 
winds at  b,  and  winds  up  at  a. 
The  weight  W  is  sustained,  one 
half  by  the  rope  d  and  the  other 
by  c;  but  as  the  rope  d  is  on  the 
same  side  of  the  fulcrum  with  the  power  P,  the  length  of  the 
short  arm  of  the  lever  is  equal  to  the  difference  between  the  ra- 
dii of  the  axle  at  a,  and  b.  This  difference  may  be  made  very 
small.  Hence  almost  unlimited  power,  coupled  with  great 
strength  of  axle,  may  be  given  to  the  .machine. 

In  this  case  a  very  heavy  weight  may  be  raised,  but  its  ve- 
locity, compared  with  that  of  the  power,  is  very  small,  so  that 
what  is  gained  in  power  is  lost  in  time.  It  is  on  this  principle 
that  a  power  which  is  variable  may  be 
made  to  exert  a  constant  force. 

This  is  exemplified  in  the  shape 
given  to  the  fusee  of  a  watch,  Fig. 
60.  The  force  of  the  main  spring,  as 
it  uncoils,  diminishes  ;  but  by  passing 
the  chain  around  the  smaller  axle, 


B 


What  limit  is  there  to  the  power  of  the  wheel  and  axle?     By  what 
What  shape  is  given  to  the  fusee  of  a  watch,  and  for  what  reason  ? 


WHEEL-WORK.  91 

when  the  force  is  most  intense,  arid  increasing  the  size  of  the 
axle  as  it  diminishes,  a  uniform  motion  is  given  to  the  hands  and 
all  the  other  parts  of  the  watch. 

4.  Communication  of  Motion  by  Wheel-work. — By  the  action 
of  two  or  more  wheels  upon  each  other,  a  very  rapid  or  a  very 
slow  movement  may  be  given  to  machinery.  If  two  wheels  of 
equal  size  touch  each  other  by  their  circumferences,  the  motion 
of  the  one,  if  there  is  considerable  friction,  will  cause  the  motion 
of  the  other  ;  or,  if  a  band  is  made  to  pass  around  two  wheels, 
motion  may  be  communicated  from  one  to  the  other,  and  their 
relative  velocities  will  depend  upon  their  size.  The  smaller 
wheel  will  move  as  much  faster  as  its  diameter  is  less. 

But  the  most  common  mode  of  communicating  motion  from 
one  wheel  to  another  is  by  means  of  teeth  cut  into  the  circum- 
ference of  one  wheel,  and  corresponding  notches,  called  leaves, 
into  the  axle  of  the  other.  This  arrangement  is  called 

Fig.  6i.  The  Wheel  and  Pinion,  Fig.  6 1 .     The 

number  of  teeth  in  the  wheel  and  of  leaves 
in  the  axle  will  be  in  proportion  to  their 
circumferences  or  to  their  radii,  and  hence 
The  product  of  the  power  into  the  num- 
ber of  teeth  in  the  wheel  will  be  equal  to  the 
product  of  the  weight  into  the  number  of 
leaves  in  the  axle. 

The  velocity  of  each  wheel  and  of  its  pinion  will  be  inversely 
as  the  number  of  teeth  ;  that  is,  the  greater  the  number  of  teeth, 
the  less  the  velocity,  and  the  reverse.  By  means  of  several 
wheels  of  different  diameters,  motion  may  be  increased  or  dimin- 
ished to  an  indefinite  extent. 

In  the  pendulum  of  the  common  clock  it  is  necessary  to  add  a 
slight  force  to  overcome  the  resistance  of  the  air  and  the  friction 
at  the  point  of  suspension. 

For  this  piirpose,  a  weight,  W,  is  applied  to  an  axle  connected 
with  a  wheel  with  teeth,  and  its  motion  is  modified  by  the  pal- 
lets, a  b,  Fig.  62,  of  the  pendulum.  When  the  pendulum  vi- 

How  can  motion  be  communicated  from  one  wheel  to  another?  De- 
scribe the  wheel  and  pinion.  What  is  the  law  of  equilibrium  ? 


92  NATURAL    PHILOSOPHY. 

brates  to  the  right,  the  pallet  a  strikes  against  a 
tooth,  and,  as  it  swings  to  the  left,  the  pallet  b 
also  presses  against  a  tooth  ;  but,  in  performing 
a  double  vibration,  one  tooth  passes  the  pallet, 
-  receiving  a^  slight  force  from  it  sufficient  to  con- 
tinue the  vibrations. 

In  order  to  communicate  a  slow  motion  to 
the  weight,  several  wheels  with  cogs  are  placed 
between  it  and  the  wheel  containing  the  teeth  ; 
by  this  means  the  weight  will  not  run  down  for 
a  day,  a  week,  and,  in  some  cases,  for  a  year. 
The  motions  of  the  hour  and  minute  hands  are 
also  regulated  by  wheels. 

Watches  and  chronometers  are  regulated  by  wheels  connected 
with  springs  instead  of  weights. 

5.  Wheel  Carriages. — The  advantages  of  wheel  carriages  over 
drags  are  twofold  :  the  friction  is  less,  and  the  power  of  the  lever 
is  used  to  overcome  obstacles. 

(1.)  It  is  evident  that  pressure  perpendicularly  downward  on 
an  even  surface  will  not  prevent  motion  in  a  horizontal  direction 
if  there  is  no  friction,  but  there  is  friction  in  proportion  to  the 
weight  and  surface.  Now  the  friction  in  a  wheel  is  not  on  the 
ground,  but  at  the  axle,  where  it  is  much  less,  and,  to  overcome 
it,  the  spokes  act  as  levers. 

(2.)  When  any  obstacle  presents  itself,  as  a  block  of  wood,  the 
load  must  be  lifted  over  it ;  the  block  becomes  a  fulcrum ;  the 
power  is  applied  at  the  axle,  on  which  the  load  rests,  and  the 
spokes  act  on  the  principle  of  the  bent  lever.  The  advantage, 
therefore,  gained  over  all  other  modes  of  surmounting  obstacles 
is  due  to  the  diminution  of  friction,  and  the  difference  between 
the  diameter  of  the  wheel  and  that  of  the  axle.  Hence  high 
wheels  overcome  obstacles  more  easily  than  those  that  are  low ; 
but  they  may  be  too  high  for  easy  draught ;  for,  besides  the  in- 
creased danger  of  upsetting,  the  line  of  draught  should  always 
ascend  from  the  axle,  so  as  to  be  at  right  angles  to  the  collar  of 
the  animal. 

How  are  the  motions  of  clock-work  rendered  uniform?  What  are  the 
advantages  of  wheel  carriages  over  drags  ?  To  what  are  these  advantages 
due? 


THE    PULLEY. 


93 


Springs  facilitate  the  motion  of  wheel  carriages,  because  they 
prevent  the  inertia  of  the  load  from  acting  suddenly  upon  the 
power.  When  the  wheel  strikes  any  obstacle,  the  shock  is  felt 
gradually.  The  center  of  gravity,  at  the  same  time,  is  lowered 
by  the  elasticity  of  the  spring,  the  load  is  not  raised  so  high,  and 
hence  less  force  is  required  to  move  it. 

III.  Pulley. — The  pulley  is  a  wheel  with  a  groove  in  its  cir- 
cumference, freely  movable  about  either  a  fixed  or  movable  pivot ; 
hence  the  pulley  is  either  fixed  or  movable :  the  latter  is  termed 
a  runner. 

The  principle  on  which  the  pulley  acts  is  the  same  as  that  of 
the  lever,  but  the  mode  of  estimating  its  power  is  different. 

Fig.  66.  Fig.  65.  Fig.  64.  Fig.  63. 


1.  Thus,  in  a  single  fixed  pulley,  Fig.  63,  the  weight  and  pow- 
er must  be  equal,  because  the  arms  of  the  lever,  a  b,  are  equal. 
There  is,  therefore,  no  advantage  in  such  a  pulley.     Its  use  is,  in 
connection  with  the  rope,  to  change  the  direction  of  motion. 

2.  But  if  one  pulley,  Fig.  64,  is  fixed  and  the  other  movable, 
then  it  is  evident  that  the  weight  will  be  divided  between  the 
two  strings,  and  in  this  arrangement  the  power  and  weight  will 
be  in  equilibrium,  when  the  poiver  multiplied  into  the  number  of 
strings  is  equal  to  the  weight ;  or,  if  a  number  of  fixed  and  mov- 

How  do  springs  facilitate  the  motion  of  wheel  carnages  ?  Describe  the 
pulley.  What  is  the  advantage  of  one  fixed  pulley  ?  What  is  the  law 
when  a  number  of  fixed  and  movable  pulleys  are  combined  ? 


94  NATURAL    PHILOSOPHY. 

able  pulleys  are  arranged  in  a  block,  as  in  Fig.  65,  the  poiver 
will  equal  the  weight  divided  by  twice  tlie  number  of  movable 
pulleys. 

3.  When  each,  movable  pulley  has  a  string  of  its  own,  Fig, 
66,  a  different  rule  must  be  found.     Thus  the  string  e  sustains 
half  the  weight,  i  also  half,  f  one  quarter,  g  one  eighth.     Each 
movable  pulley  divides  the  weight,  or  the  power  is  to  the  weight 
in  the  first  pulley  as  1  to  2,  in  the  second  as  1  to  2,  and  in  the 
third  as  1  to  2.     Therefore  the  power  is  to  the  weight  as  1  to 
2x2x2  —  8,  or  as  1  to  8. 

It  will  be  seen  that  2  is  raised  to  a  power  represented  by  the 
number  of  movable  pulleys,  in  this  case  the  third  power  of  2. 
If  there  are  four  movable  pulleys,  2  must  be  raised  to  the  fourth 
power.  Hence,  in  this  system  of  pulleys,  there  will  be  an  equi- 
librium of  the  power  and  weight 

When  the  weight  equals  the  product  of  2,  raised  to  a  power 
represented  by  the  number  of  movable  pulleys,  multiplied  into 
the  power. 

Prob.  1.  A  weight  of  ten  tons  was  sustained  by  a  system  of 
four  movable  pulleys.  What  was  the  power  ? 

Ans.,  1250  Ibs. 

2.  What  weight  could  a  man  weighing  200  Ibs.  raise  by 
means  of  a  system  of  five  movable  pulleys  ?  Ans.,  6400  Ibs. 

4.  In  all  the  above  cases  the  strings  are  F-     67 
parallel  to  each  other,  but,  in  case  their 

action  is  oblique,  then  the  force  which  sus-  •"• 
tains  the  weight  must  be  resolved  into  two 
others.  Thus,  let  the  strings  A/,  B/act 
obliquely  on  the  weight  around  the  pulley, 
e,  Fig.  67.  Let  e  f  represent  the  force 
acting  in  the  direction  eB.  This  force 
may  be  resolved  into  c  e  and  cf.  cf  will 
represent  the  force  which  the  string  B  e 
sustains,  equal  to  half  the  weight;  hence 
%cf  will  represent  the  force  which  sustains 
the  whole  weight.  We  then  have  the  pro- 
portion P  :  W  :  :  ef :  %cf;  or,  as  radius  to 
twice  the  cosine  of  the  angle  cfe,  or  twice  I*\~W 

the  cosine  of  the  angle  made  by  the  lines 
which  represent  the  direction  of  the  power  and  the  weight. 

5.  Uses  of  the  Pulley. — The  pulley  is  one  of  the  most  useful 
of  the  mechanical  powers.  In  loading  and  unloading  ships,  rais- 

What  is  the  law  \vhen  each  movable  pulley  has  a  string  of  its  own  ? 


THE    INCLINED    PLANE. 


ing  weights,  moving  of  buildings,  and,  g 
resistance  is  to  be  overcome,  the  pulley  is  either 
in  connection  with  the  other  mechanical  powers. 

It  has  a  great  advantage  over  the  lever,  by  furnishing  a  ready 
means  of  changing  the  direction  of  motion.  But  its  mechanical 
advantage  is  the  same  as  that  of  all  machines  :  what  is  gained 
in  power  is  lost  in  time.  If  one  man,  by  means  of  a  system  of 
pulleys,  can  raise  a  weight  through  a  given  space  which  would 
require  ten  to  lift,  it  will  take  him  ten  times  as  long  to  do  it ;  in 
other  words,  the  power  must  move  as  much  faster  than  the  weight 
as  its  quantity  of  matter  is  less.  In  the  use  of  the  pulley,  as  in 
that  of  the  wheel  and  axle,  allowance  must  be  made  for  the  ri- 
gidity of  the  cordage,  and  for  the  diameter  of  the  rope,  half  of 
which  must  be  added  to  the  radius  of  the  wheel,  and  also  to  the 
radius  of  the  axle ;  and,  in  order  to  produce  motion  of  the  weight, 
a  slight  force  must  be  added  to  the  power. 

SECTION  II.— OF  THE  INCLINED  PLANE,  THE  SCREW,  AND  THE  WEDGE. 

I.  In  the  inclined  plane,  the  power  may  act  parallel  to  the 
plane,  or  parallel  to  the  base  of  the  plane,  or  at  any  angle  with 
the  weight. 

1 .  In  the  first  case,  the  power  multiplied  into  the  length  of 
the  plane  equals  the  weight  multiplied  into  its  height. 

2.  In  the  second  case,  the  power  is  equal  to  the  weight  multi- 
plied into  the  height  of  the  plane,  and  divided  by  the  length  of 
the  base. 

II.  The  screw  acts  on  the  same  principle  with  the  inclined 
plane,  and  there  will  be  an  equilibrium  of  the  power  and  the 
weight  when  the  poiver,  multiplied  into  the  circumference  of  the 
base,  is  equal  to  the  weight  midtiplied  into  the  distance  between 
two  contiguous  threads. 

III.  The  wedge  is  two  inclined  planes  combined,  and  the  pow- 
er multiplied  into  the  length  of  the  wedge  will  equal  the  weight 
multiplied  into  one  half  the  height  of  the  back. 

In  practical  mechanics,  a  slight  force  must  be  added  in  all 
the  above  cases  to  the  power,  to  overcome  friction  and  to  give  mo- 
tion to  the  weight. 


96 


NATURAL    PHILOSOPHY. 


Fig.  68. 


I.  Inclined  Plane. — In  the  inclined  plane  the  power  and  the 
weight  are  in  equilibrium,  or  balance  each  other,  on  the  general 
principle  which  applies  to  all  machines.  Notwithstanding  the 
plane  may  be  at  any  angle  from  0°  to  90°,  and  the  power  ma$r 
act  at  any  angle  or  parallel  to  the  plane,  the  problem  of  the  equi- 
librium of  the  power  and  weight  admits  of  a  general  solution. 

But  it  is  more  practical  to  obtain  a  rule  for  each  of  the  modes 
in  which  the  power  acts  upon  the  weight ;  for  the  power  may 
act  parallel  to  the  plane,  or  parallel  to  the  base  of  the  plane,  or 
at  any  angle  with  the  weight. 

1 .  When  the  poiver  acts  parallel  to  the  plane,  it  is  easy  to  as- 
certain the  conditions  of  equilibrium. 

Let  ABC,  Fig.  68, 
be  an  inclined  plane,  so 
constructed  that  A  C 
may  be  raised  to  any  an- 
gle that  maybe  required, 
W  the  weight,  and  P  the 
power,  acting  by  means 
of  a  pulley  parallel  to 
the  plane.  Let  e  h,  per- 
pendicular to  the  base  A 
B,  represent  the  direc- 
tion and  force  of  gravity  which  causes  the  body  to  descend.  This 
force  may  be  resolved  into  two  others  :  e  i,  acting  perpendicular- 
ly to  the  plane  A  C,  and  h  i,  acting  parallel  to  it.  h  i  will  equal 
the  force  which  impels  the  load  down  the  plane,  e  i  the  pressure 
upon  the  plane  represented  by  p,  and  e  h  the  weight  W. 

(1)  Now  the  triangles  e  h  i  and  ABC  are  similar,  and  we  have 
the  proportions  hi  :  eh  : :  CB  :  AC,  or  P  :  W :  :  CB  :  AC.    That  is, 

The  power  is  to  the  weight  as  the  height  of  the  plane  to  its 
length.  If,  therefore,  the  length  be  twenty  feet  and  the  height 
ten,  the  power  will  be  one  half  of  the  weight. 

(2)  From  the  same  triangles  we  have  the  proportion  hi  :  ei  :  : 
BC  :  AB,  or  P  \p  : :  BC  :  AB.     Hence  the  power  is  to  the  press- 
ure as  the  height  of  the  plane  to  its  base. 

By  multiplying  the  extremes  and  means  in  the  above  proportions,  we  de- 
rive the  following  formulae : 

What  are  the  laws  of  equilibrium  when  the  power  acts  parallel  to  the 
plane  ? 


THE    INCLINED    PLANE.  97 

P  xlength=W  X  height. 
P  X  base=p  X  height. 

It  will  be  seen  that  if  any  three  parts  are  known,  the  other  may  be  found. 
Thus,  if  the  height,  length  of  the  plane,  and  the  weight  are  given,  the  pow- 

•i     A  «-        •     A     t     t>     WXheight 
er  can  be  easily  determined  ;  tor  r—  —  =  -  £=  —  . 

length 

If  the  height,  length,  and  power  are  known,  the  weight  may  be  found: 


height 

(3)  If  we  represent  the  angle  B  A  C  by  x,  we  may  derive  a  general  expres- 
sion for  every  angle  which  the  plane  makes  with  the  base  ;  for  hi  :  BO  :  : 
eh  :  AC,  or  P  :  sin.  a?  :  :  W  :  R  or  1,  P  X  R=sin.  of  xX  W  ;  that  is, 

The  force  which  urges  the  weight  down  the  plane  is  equal  to  the  weight 
into  the  sine  of  the  angle  of  elevation. 

We  have  also  the  proportion  ei  :  eh  :  :  AB  :  AC,  or  p  :  W  :  :  cos.  x  :  R 
or  1  ;  .-.  £>xR  or  l=cos.  ,#xW.  That  is, 

The  pressure  of  the  weight  on  the  plane  equals  the  weight  multiplied  into 
the  cosine  of  the  angle  of  elevation. 

By  using  the  little  carriage  represented  in  the  figure,  and  placing  weights 
in  it,  these  laws  may  be  illustrated  by  experiment. 

Exp.  —  Place  a  weight  in  the  little  carnage,  which,  with  the  carriage, 
weighs  fifty  ounces,  and  elevate  the  plane  to  an  angle  of  30°  ;  then  the  sine 
of  this  angle  will  be  equal  to  half  of  radius,  or  half  A  C,  and  hence  hi—beh. 
That  is,  the  force  which  urges  the  carriage  down  the  plane  is  equal  to  half 
of  the  weight,  and  therefore  the  power  required  to  balance  fifty  ounces  is 
only  twenty  -five  ounces.  For  any  other  angle  the  computations  are  easily 
made,  though  these  computations  require  some  knowledge  of  trigonometry. 

(4)  When  the  power  acts  at  any  angle  with  the  weight,  we  have  only  to  sub- 
stitute the  sine  of  this  angle  for  radius  in  the  above  proportions  to  determ- 
ine the  relation  of  the  power  and  weight,  and  then  we  shall  have  an  equi- 
librium 

When  the  power  is  to  the  weight  as  the  sine  of  the  angle  of  elevation  to  the 
sine  of  the  angle  made  by  the  direction  of  the  power  with  a  perpendicular  to 
the  plane  at  the  point  where  the  weight  rests.  If  we  represent  this  last  angle 

by  y,  then  P  :  W  :  :  sin.  x  :  sin.  y  ;  .:  W  X  sin.  x=P  X  sin.  y,  W—  E>XS1"'y, 

and  P=r  —  .  -  -  —  ,  and  the  pressure  on  the  plane  will  equal  »=  —  XCQS.  x 
sin.  y  sin.  y 

PROBLEMS. 

1.  A  train  of  loaded  cars,  weighing  300  tons,  were  drawn  up  an  inclined 
plane  whose  angle  of  elevation  was  40°  ;  what  was  the  power  exerted  by 
the  engine  ? 

Ans.,  192-803-J-  tons 

2.  To  what  was  the  pressure  of  the  cars  in  the  above  example  equal? 

Ans.,  229-9-}-  tons. 

3.  In  raising  a  vessel  on  an  inclined  plane  at  an  angle  of  3°,  it  was  nec- 
essary to  exert  a  power  of  2QOO  Ibs.     How  much  did  the  vessel  weigh  ? 

Ans.,  38210-f-lbs. 
What  was  its  pressure  on  the  plane  ? 

Ans.,  38160+  Ibs. 

How  much  power  would  have  been  required  if  the  vessel  had  been  rais- 
ed by  a  block  of  five  movable  pulleys? 

Ans..    62  A  Ibs, 

E  - 


NATURAL   PHILOSOPHY. 


4.  On  a  plane  inclined  at  an  angle  of  10°,  two  men  exerted  a  force  of 
300  Ibs.  by  means  of  a  rope  passed  over  a  fixed  pulley,  the  rope  making 
an  angle  with  the  plane  of  8°.     What  was  the  value  of  the  weight  ? 

Ana.  17  01+ Ibs. 

5.  What  was  the  pressure  of  the  weight  on  the  plane  in  the  above  ex- 
ample ? 

2.  When  the  power  acts  parallel  to  the  base  of  the  plane. 

When  the  power  is  applied  in  a  direction  parallel  to  the  base 
of  the  plane,  the  relation  of  the  power  to  the  weight  may  be  de- 
termined in  the  same  manner  with  the  preceding ;  for,  producing 
e  i  to  g,  and  drawing  h  g 
perpendicular  to  B  c.  Fig. 
69,  we  shall  have  the  sim- 
ilar triangles  ABC  and 
e  h  g.  h  g  will  equal 
the  power  and  e  h  the 
weight.  We  shall  then 
have  the  proportion  hg  : 
eh  :  :  BC  :  AB  ;  or, 

The  power  is  to  the    A 
weight  as  the  height  of  the  plane  to  its  base. 

From  the  same  triangles  we  shall  also  have  the  proportion 
kg:  eg::  BC  :  AC ;  or,  as  eg  is  equal  to  the  pressure  on  the  plane, 

The  power  is  to  the  pressure  as  the  height  of  the  plane  to  its 
length. 

Finally,  eh  :  eg  \  :  AB  :  AC  ;  or,  as  eh  is  equal  to  the  weight, 

The  weight  is  to  the  pressure  as  the  base  of  the  plane  to  its 
length. 

From  these  proportions,  by  multiplying  the   extremes   and 
means,  we  derive  the  following  formulae  : 
P  X  base = W  X  height. 
P  X  length— pressure  X  height. 
W  X  length = pressure  X  base. 

The  mathematical  deductions  which  are  derived  from  the 
inclined  plane  are  easily  illustrated  by  experiment.  It  may  also 
be  proved  that  the  power  to  sustain  a  given  weight  is  least  when 


What  are  the  laws  of  equilibrium  when  the  power  acts  parallel  to  the 
base  of  the  plane  ? 


PROBLEMS.  99 

its  action  is  parallel  to  the  plane,  and  greatest  when  the  line  of 
force  is  parallel  to  the  base  of  the  plane. 

PROBLEMS. 

1.  If  an  inclined  plane  is  50  feet  long  and  10  feet  high,  what 
power  acting  parallel  to  the  plane  will  balance  a  weight  of  20 
tons  ?  Am.  4  tons. 

2.  What  would  the  pressure  be  equal  to  in  the  above  example  ? 

3.  A  train  of  baggage  cars,  passing  down  on  an  inclined  plane 
300  feet  long  and  30  feet  high,  was  held  back  by  an  engine  which 
exerted  a  force  of  10  tons  ;  what  was  the  weight  of  the  train  ? 

Ans.  100  tons. 

4.  If  the  length  of  a  plane  is  500  feet,  the  weight  of  a  train  of 
cars  400  tons,  and  the  force  10  tons,  what  is  the  height  of  the 
plane  ? 

Ans.  121  feet. 

5.  If  the  height  of  a  plane  is  20  feet,  the  weight  500  tons,  and 
the  power  20  tons,  what  is  the  length  of  the  plane  ? 

Ans.  500  feet. 

6.  If  the  pressure  on  a  plane  is  200  tons,  the  height  40  feet, 
and  tfye  power  5  tons,  what  is  the  length  of  the  base  ? 

Ans.  1600  feet. 

7.  An  inclined  plane  is  10  feet  long  and  6  feet  high  ;  what 
power  acting  parallel  to  the  base  would  sustain  30  tons  ? 

Ans.  22±  tons. 

8.  What  would  the  pressure  in  the  above  example  be  equal  to  ? 

Ans.  37^  tons. 

9.  In  an  inclined  plane  25  feet  long  and  7  feet  high,  what 
weight  would  a  force  of  200  Ibs.  sustain  acting  parallel  to  the 


Ans.  685f  Ibs. 

3.  Uses  of  the  Inclined  Plane. — The  inclined  plane  is  much 
used  in  the  arts.  Roads  leading  up  the  sides  of  hills  are  inclined 
planes,  and  the  force  necessary  to  draw  heavy  wagons  up  these 
planes  must  be  sufficient  not  only  to  overcome  the  friction,  but  to 
sustain  that  portion  of  the  force  of  gravity  which  acts  parallel  to 
Mention  the  uses  of  the  inclined  plane. 


100  NATURAL    PHILOSOPHY. 

the  plane,  and  which,  of  course,  increases  with  the  steepness  of 
the  ascent.  Where  the  hill  is  very  steep,  the  road  is  made  to 
wind  around  it,  by  which  its  steepness  is  greatly  diminished.  It 
is  supposed  that  the  ancient  Pyramids  of  Egypt  were  built  by 
means  of  inclined  planes,  up  which  those  ponderous  masses  of 
rock  were  raised  to  their  present  position. 

Railways  consist  of  a  series  of  inclined  planes,  generally  vary- 
ing but  little  from  a  horizontal  plane,  but  in  some  cases  so  in- 
clined as  to  require  stationary  engines  to  draw  up  and  let  down 
trains  of  cars.  By  means  of  steam  power,  hundreds  of  tons  are 
transported  by  a  single  engine.  The  speed,  also,  has  been  great- 
ly increased,  amounting  to  20,  30,  and,  in  some  cases,  60  miles 
an  hour. 

4.  Motion  down  Inclined  Planes. — Having  investigated  the 
laws  of  the  equilibrium  of  the  power  and  weight  on  inclined 
planes,  let  us  now  ascertain  the  laws  which  govern  the  motions 
of  bodies  descending  planes  of  different  elevations. 

Let  ABC,  Fig.  70,  be  an  inclin- 
ed  plane,  and  a  weight,  W,  just  bal- 
anced by  the  power,  P.  We  have 
found,  p.  96,  that  P  :  W  : :  CB  :  AC. 

Now  the  force  with  which  the 
weight  W  tends  to  fall  down  A  C 
will  be  to  its  weight  as  CB  :  to  AC  ; 
hence 

The  force  which  urges  any  body  down  an  inclined  plane  is  to 
the  force  of  gravity  as  the  height  of  the  plane  to  its  length. 

Let  H  =  the  height  and  L  =  the  length  of  the  plane,  F  =  the 
force  which  urges  the  body  down  the  plane,  and  1  =  to  gravity  ; 

TT 

then  F  :  1  :  :  H  :  L,  or  F  =  — .     Hence  we  may  always  ascer- 

L 

tain  the  force  which  urges  a  body  down  an  inclined  plane,  what- 
ever the  inclination  may  be,  by  dividing  the  height  of  the  plane 
by  its  length  (gravity  being  1). 

As  the  velocity  of  any  body  depends  upon  the  intensity  of  the 
forces  acting  upon  it,  and  the  time  they  have  acted, 

What  law  governs  the  motion  of  bodies  down  inclined  planes  ?  What 
does  the  velocity  of  a  body  depend  upon? 


THE    INCLINED    PLANE. 


101 


The  velocity  generated  by  a  body  falling  down  an  inclined 
plane,  as  A  C,  is  equal  to  that  acquired  by  falling  freely  through 
the  height  of  the  plane  C  B ;  for  the  times  are  found  to  be  as  the 
length  to  the  height,  and  the  forces  are  also  as  the  length  to  the 
height,  and  hence  the  velocities  must  be  equal. 

It  may  also  be  shown  that  the  spaces  described  by  bodies  fall- 
ing down  inclined  planes  vary  as  the  squares  of  the  times — the 
same  law  which  applies  to  bodies  falling  freely  by  the  force  of 

TT 

gravity — that  is,  S  =  —  -f  gT2 ;  but  HLg  are  known,  and  hence 
Ju 

S  varies  as  T2,  page  66.  Hence  the  spaces  described  in  equal 
successive  portions  of  time  are  as  the  numbers  1,  3,  5, 7,  9,  &c.  It 
is  found,  also,  that  the  time  varies  as  the  length  of  the  plane,  and 
inversely  as  the  square  root  of  its  height,  and  that  the  velocity 
varies  as  the  square  root  of  its  height. 

The  motion  of  bodies  down  several  planes  differently  inclined 
depends  upon  similar  laws. 

Thus,  let  Ae^C,  Fig.  71, 
be  a  series  of  inclined  planes  : 
it  is  evident,  from  what  has 
been  previously  stated,  that 
the  velocity  acquired  by  falling 
down  C  d,  d  e,  e  A,  would  be 
a  equal  to  that  acquired  by  fall- 
"  ing  through  the  several  heights 
of  those  planes,  Cf,fg,  gift, 
B  or  the  velocity  in  falling  from 
C  to  A  would  equal  that  acquired  in  falling  from  C  to  B. 

If,  now,  the  number  of  planes  be  indefinitely  increased,  they 
will  form  a  curve,  A  C,  Fig.  72,  and  hence 

The  velocity  acquired  by  any  body  in  falling 
through  a  curve  is  equal  to  that  acquired  in  fall- 
ing through  the  perpendicular  height  of  the  curve. 
From  this  point  we  may  examine  the  proper- 
ties and  uses  of 

5.  The  Pendulum. — The  pendulum  is  a  heavy 
ball,  suspended  by  a  flexible  thread  from  a  point 


Fig.TL 


Fig.  72. 


What  velocity  does  a  body  acquire  in  falling  down  an  inclined  plane? 
What  law  is  observed  by  bodies  falling  down  different  systems  of  inclined 
'     Describe  the  pendulum. 


102 


NATURAL    PHILOSOPHY. 


about  which  it  has  a  free  motion,  as  A 
B,  Fig.  73. 

If  B  be  raised  to  D,  and  allowed  to 
fall,  the  force  of  gravity  will  cause  it  to 
descend  through  the  arc  DEC,  acquir- 
ing at  the  point  C  a  velocity  which  will 
carry  it  to  G,  equal  to  the  height  from 
which  'it  fell.  This  motion  through  the 
arc  D  C  G  is  called  a  vibration  or  oscil- 
lation. From  G  the  pendulum  will  de- 
scend again  through  the  arc  to  D,  and 
thus  it  would  continue  to  vibrate  forever  were  there  no  friction 
at  A,  and  no  resistance  of  the  air ;  but,  in  consequence  of  these 
obstacles,  the  lengths  of  its  oscillations  grow  less  and  less,  until  it 
is  brought  to  a  state  of  rest  at  C. 

To  keep  up  the  vibrations  in  our  common  clocks,  a  slight  force 
is  applied  by  means  of  a  wheel,  which  acts  upon  the  pallets  of 
the  pendulum  (page  92). 

Center  of  Oscillation. — If  we  suppose  the  rod  A  C  to  be  destitute  of 
weight  and  a  single  atom  to  be  suspended  from  its  point,  it  would  constitute 
a  simple  pendulum;  but  the  rod  consists  of  a  series  of  such  atoms,  and  hence 
the  pendulum  A  C  is  compound.  The  parts  near  A  tend  to  vibrate  more 
rapidly  than  those  near  C,  and  hence  tend  to  increase  their  motion,  while 
the  parts  near  C  tend  to  diminish  the  motion  of  the  parts  near  A.  There 
must  be  some  point  between  A  and  C  which  vibrates  exactly  as  fast  as  a 
simple  pendulum  whose  length  is  equal  to  its  distance  from  A,  and  this 
point  is  called  the  center  of  oscillation.  This  point  describes  the  arc  G  C  D. 
It  is  a  difficult  problem  practically  to  determine  this  point.  In  most  pend- 
ulums the  center  of  oscillation  lies  a  little  below  the  center  of  gravity. 

In  the  pendulum  the  laws  of  oscillation  are  generally  derived 
from  the  properties  of  the  cycloid. 

This  is  a  curve  described  by  a 
fixed  point,  as  P,  Fig.  74,  in  the  cir- 
cumference of  a  circle  as  it  rolls  on 
a  plane,  as  from  D  to  B.  It  is  the 
jurve  of  swiftest  descent ,  and  the  vi- 
brations of  a  pendulum,  whether  longer  or  shorter,  in  such  an 
arc  are  all  exactly  equal.  In  a  circular  arc  there  is  a  slight  va- 
riation. It  is  found  by  experiment,  however,  that  when  the  vi- 
brations are  through  a  small  part  of  the  arc  of  a  circle,  there  is 
but  a  slight  error,  which  may  easily  be  corrected,  for  the  arc  of 
the  cycloid  and  the  laws  of  vibration  accurately  deduced. 

What  and  where  is  the  center  of  oscillation  ?  Why  do  the  vibrations 
cease  ?  How  is  a  cycloid  arc  produced  ?  In  what  arc  are  the  vibrations 
of  a  pendulum  equal  ? 


Fig.  74. 


THE    PENDULUM. 


103 


(1.)  The  duration  of  the  oscillations  of  a  pendulum  is  not  in- 
fluenced  by  its  iveight  or  by  the  nature  of  its  substance.  This 
law  is  easily  proved  by  experiment ;  for  if  we  take  several  pendu- 
lums of  equal  lengths,  but  of  different  weight  and  substance,  their 
vibrations  will  be  exactly  equal.  This  shows  that  the  force  of 
gravity  is  the  same  for  all  kinds  of  matter. 

(2.)  The  oscillations  of  a  pendulum,  are  all  equal  in  duration, 
whether  they  are  performed  through  the  less  or  the  greater  arc. 
Thus  the  vibrations  in  the  arc  D  G,  Fig.  73,  will  be  performed 
in  the  same  time  with  those  in  the  arc  F  E.  This  law  is  proved 
by  noticing  a  great  number  of  vibrations,  and  observing  accu- 
rately the  time  of  each.  The  'reason  of  this  law  is  simply  this, 
that  in  the  longer  vibrations  the  velocity  is  so  much  greater  than 
in  the*  shorter,  that  they  are  performed  in  the  same  time. 

(3.)  The  duration  of  the  vibrations  of  a  pendulum  depends 
upon  its  length.  The  longer  the  pendulum,  the  slower  are  its 
oscillations.  This  law  is  also  proved  by  experiment. 

(4.)  The  oscillations  of  two  pendulums  of  unequal  lengths  are 
to  each  other  inversely  as  the  square  roots  of  their  lengths.  That 
is,  if  we  compare  any  two  pendulums,  Fig. 
75,  one  and  four,  or  one  and  nine  feet  in 
length,  their  oscillations  will  be  inversely 
as  the  square  roots  of  their  lengths.  Thus, 
while  the  pendulum  which  is  four  feet 
makes  one,  that  which  is  one  foot  will  make 
"two  oscillations,  and  while  that  which  is 
nine  feet  makes  one,  that  which  is  one  will 
make  three  oscillations.  A  pendulum,  there- 
fore, which  beats  seconds,  must  be  four  times 

*  ^      as  long  as  one  that  beats  half  seconds,  arid 

V'      one  which  beats  once  in  two  seconds  must  be 
four  times  as  long  as  one  which  beats  seconds. 

6.  Uses  and  Applications  of  the  Pendulum. — The  p'endulum 
is  used  for  three  most  important  purposes  :  1.  As  a  measure  of 
time.  2.  To  determine  the 'form  of *the  earth.  3.  To  fix  a  stand- 
ard of  weights  and  measures. 

Upon  what  does  the  duration  of  the  vibrations  of  a  pendulum  depend  ? 

„  What  relation  do  the  vibrations  of  pendulums  of  different  lengths  bear  to 

each  other  ?     How  much  faster  will  a  pendulum  one  foot  in  length  vibrate 

than  one  four  feet  in  length  ?  than  one  nine  feet  in  length  ?    What  are  the 

uses  of  the  pendulum? 


104 


NATURAL    PHILOSOPHY. 


(1.)  As  a  Measure  of  Time. — Galileo  made  the  rirst  observa- 
tions on  this  subject  by  noticing  that  the  oscillations  of  a  lamp  in 
a  church  were  nearly  equal.  He  applied  this  knowledge  to  the 
measure  of  time,  but  Huygens  first  made  use  of  clock-work  in  or- 
der to  render  the  vibrations  constant  and  to  register  their  number. 

Pendulums  which  beat  seconds,  that  is,  which  occupy  y^  o^th 
part  of  a  mean  solar  day  in  one  vibration,  are  39-11  inches  in 
length,  though  their  length  varies  a  little  in  going  from  the  equa- 
tor to  the  pole.  As  heat  expands  the  metal  out  of  which  they 
are  constructed,  thus  making  it  longer,  and  as  cold  contracts  it, 
thus  making  it  shorter,  there  arise  slight  inaccuracies,  which  are 
remedied  by  means  of  compensation  pendulums,  the  principal  of 
which  are  the  Mercurial  Pendulum  and  the 

Gridiron  Pendulum*  —  The  compensation  is  effected  by 
combining  two  or  more  metals,  which  are  expanded  differently 
by  the  same  degree  of  heat,  in  such  a  manner  that  their  expan- 
sions shall  mutually  counteract  each  other,  and  keep  the  center 
of  oscillation  at  the  same  distance  from  the  point  of  suspension. 

Steel  and  brass  are  the  metals  usually  combined.  If  the  ex- 
pansion for  brass  be  represented  by  100,  that  of  steel  will  be  about 
6 1 .  Then,  by  making  the  pendulum  rods 
100  parts  of  steel  and  61  of  brass,  and  so 
arranging  them  that  one  shall  expand  up- 
ward and  the  other  downward,  their  ex- 
pansions will  exactly  compensate  for  each 
other. 

Thus,  the  steel  bars  s  s,  Fig.  76,  ex- 
pand only  downward,  and  the  brass,  b  b, 
only  upward ;  and  as  the  expansions  up- 
ward are  just  equal  to  the  expansions 
downward,  the  length  of  the  pendulum 
remains  constant  under  all  the  variations 
of  temperature.  By  this  contrivance  the 
pendulum  becomes  the  most  accurate 
measurer  of  time. 

*  So  named  because  it  resembles  the  gridiron. 


How  long  must  it  be  to  beat  seconds  ?     What  are  the  causes  of  inaccu- 
racy in  the  pendulum  1     Describe  the  gridiron  pendulum. 


USES    OF    THE    INCLINED    PLANE.  105 

(2.)  The  pendulum  is  used  to  determine  the  figure  of  the  earth, 
and  this  is  one  of  its  most  interesting  applications.  The  length 
being  the  same,  the  frequency  of  the  vibrations  at  any  place  on 
the  earth's  surface  will  depend  upon  the  intensity  of  the  force 
of  gravity  at  that  place.  As  this  force  is  inversely  as  the  square 
of  the  distance  from  the  center  of  the  earth,  if  one  portion  of  the 
earth's  surface  is  nearer  than  another  portion  (conceiving  the  whole 
force  of  attraction  to  be  situated  at  the  center  of  the  earth),  the 
vibrations  of  the  pendulum  will  be  more  rapid  at  that  point. 

Now  it  is  found  by  observation,  that  as  we  go  from  the  equa- 
tor to  the  pole,  the  vibrations  are  gradually  increased  in  frequen- 
cy, which  shows  that  the  poles  are  nearer  the  center  of  the  earth 
4han  the  equator  by  about  17  miles.  By  measurement  of  arcs 
of  the  meridian,  the  difference  is  a  little  less,  being  only  13  miles. 

(3.)  The  last  and  a  very  important  use  of  the  pendulum  is  to 
fix  a  standard  of  measure  and  of  weight.  The  only  standard 
which  is  not  liable  to  vary  is  derived  from  the  revolutions  of  the 
earth.  The  pendulum  which  beats  seconds,  or  which  measures 
•^g-i^ths  of  a  mean  solar  day,  is,  as  we  have  seen,  39'11  inches 
in  length.  The  linear  yard  is  a  little  less,  having  the  ratio  of  1 
to  1-086158,  or  36  inches.  When  such  a  measure  is  accurately 
made  at  the  temperature  of  melting  ice,  it  may  be  used  for  a 
long  time  as  a  standard  ;  but,  as  it  may  vary,  it  is  easy  to  verify 
or  correct  it  by  a  standard  pendulum.  There  is  one  kept  in  Co- 
lumbia College,  New  York  city,  which  beats  seconds,  the  .oscil- 
lations being  performed  in  a  cycloidal  arc,  and  also  in  a  vacuum. 

Having  fixed  upon  the  length  of  the  yard,  it  may  be  subdivid- 
ed into  feet,  inches,  &c.  From  linear  measure,  square  measure, 
or  the  measure  of  surfaces,  is  directly  derived,  and  also  solid 
measure. 

But  how  shall  we  derive  a  standard  of  weights  from  the 
length  of  a  yard  or  the  revolution  of  the  earth  ?  This  is  done 
by  taking  a  box  containing  just  one  cubic  foot,  or  twelve  linear 
inches  in  length,  breadth,  and  height,  filling  it  with  distilled  wa- 
ter, and  counterpoising  it  by  a  bar  of  lead  or  some  other  metal. 

Describe  the  process  by  which  the  shape  of  the  earth  is  determined. 
How  is  the  standard  of  weight  and  measure  determined  ? 

E  2 


106  NATURAL    PHILOSOPHY. 

This  bar  is  then  divided  into  1000  equal  parts,  and  these  are 
called  ounces.  Sixteen  of  these  make  a  pound  avoirdupois,  and 
from  these  all  other  measures  and  weights  are  derived. 

A  gallon  of  dry  measure  holds  10  Ibs.  of  distilled  water  ;  a 
bushel,  80  pounds.  A  gallon  of  liquid  measure  contains  8  Ibs.  of 
distilled  water.  In  all  these  cases  the  water  is  taken  at  its  max- 
imum density,  which  is  about  40°  F. 

The  standards  adopted  by  the  United  States  are  as  follows  : 

1 .  Of  Length. — The  yard  of  3  feet,  taken  from  Troughton's 
brass  scale,  which  is  82  inches  in  length.     This  is  the  same  as 
the  imperial  standard. 

2.  Of  Weight. — The  Troy  pound,  or  5762-38  grs.,  is  used  for 
a  standard  at  the  Mint  of  the  United  States.  • 

3.  Of  Dry  Measure. — The  Winchester  bushel,  which  contains 
2150-4  cubic  inches. 

4.  Of  Liquid  Measure. — The  English  wine  gallon,  containing 
231  cubic  inches. 

All  merchandise,  however,  is  bought  and  sold  by  avoirdupois 
•weight,  a  pound  being  7680  grs. 

Iir  The  Screw. —  The  screw  is  an  inclined  plane  wound 
around  a  cylinder.  It  generally  consists  of  a  spiral  groove  cut 
either  into  the  convex  or  concave  surface  of  a  cylinder ;  in  fact, 
the  action  of  a  screw  requires  both  to  be  united.  That  on  the 
concave  surface  is  called  the  nut. 

The  thread  of  a  screw  may  be  triangular  or  flat. 

The  law  of  equilibrium  in  the  screw  is  the  same  as  that  of  the 
inclined  plane,  where  the  power  acts  parallel  to  the  base.  Thus, 

Let  the  inclined  plane,  A  Fi.rt. 

B  C,  Fig.  77,  be  wound 
around  the  cylinder  D,  which 
has  a  base  equal  in  circumfer- 
ence to  the  base  of  the  plane 
A  B.  The  line  A  C  will  rep- 
resent the  threads  of  the  screw, 
and  B  C  the  distance  between 
them,  1,  2,  3.  Now,  by  ap- 

Mentiou  the  different  standards  of  weight  and  of  measure.  Describe  the 
screw.  On  what  principle  does  it  act  ?  What  is  the  law  of  equilibrium  ? 


THE    SCREW. 


107 


Fig.  is. 


plying  the  principle,  The  power  is  to  the  weight  as  the  height  of 
the  plane  to  its  base,  we  shall  find  that  an  equilibrium  will  be 
produced  when 

1.  The  power  is  to  the  weight  as  tlie  distance  between  two  con- 
tiguous threads  to  the  circumference  of  the  base. 

The  screw,  when  used  as  a  mechanical  power,  is  elevated  and 
depressed  by  being  turned  within  a  concave 
nut,  b,  Fig.  78,  and  for  turning  it  a  lever,  a,  is 
usually  employed,  so  that  the  screw  combines 
the  advantages  of  the  lever  and  inclined  plane. 
Hence  the  power  which  a  screw  is  capable  of 
exerting  will  be  increased  over  that  of  the  in- 
clined plane  in  the  ratio  of  the  length  of  the 
lever  to  the  radius  of  the  cylinder.  In  this 
case  it  is  found  that  equilibrium  is  maintained  when 

2.  The  power  is  to  the  weight  as  the  distance  between  two  con- 
tiguous threads  to  the  circumference  of  a  circle  made  by  one  rev- 
olution of  the  power. 

PROBLEMS. 

1.  In  pressing  a  bale  of  cotton  by  a  screw,  the  distance  of 
whose  threads  was  1  inch,  a  power  of  300  Ibs.  was  applied  on 
the  end  of  a  lever  10  feet  long  ;  what  was  the  amount  of  press- 
ure exerted  ? 

Ans.  113-0976  tons. 

2.  What  power  must  be  applied  in  the  above  example  to  exert 
a  pressure  of  20  tons  ? 

FY^.79.  Ans.  53-05+  Ibs. 

f!        .vivSL         Jl  The  screw  is  generally  used  for  the  pur- 

Upose  of  compression  ;  but  it  matters  not 
how  the  power  is  applied,  for  a  force  that 
will  lift  a  weight  of  ten  tons  will  impart 
the  same  amount  of  pressure. 

The  endless  screw,  Fig.  79,  combined 
with  the  wheel  and  axle,  is  employed  for 
certain  purposes,  and  is  capable  of  exert- 
ing great  pressure. 

What  two  mechanical  powers  are  combined  in  the  screw?    For  what  is 
the  screw  employed  ? 


108 


NATURAL    PHILOSOPHY. 


It  will  be  noticed  that  the  power  of  the  screw  depends  upon 
the  distance  between  the  threads  and  the  length  of  the  lever.  If 
the  threads  are  very  near  each  other,  one  revolution  of  the  power 
will  raise  the  weight  but  a  short  distance,  and  hence  but  little 
power  will  be  required ;  or,  if  the  lever  is  very  long,  the  power 
required  to  turn  the  screw  will  be  proportionably  diminished. 
Now,  by  diminishing  the  distance  between  the  threads,  their  size 
will  at  length  become  too  small  to  sustain  any  great  resistance, 
and  a  very  long  lever  is  inconvenient,  because  the  power  must 
travel  over  too  great  a  space. 

What  we  need  is  compactness  and  strength  connected  with 
great  power,  and  this  has  been  achieved 
by  Hunter's  Screw,  Fig.  80,  which  acts 
on  the  principle  of  the  wheel  and  axle, 
page  89.  This  screw  is  composed  of  two 
parts,  consisting  of  larger  and  smaller 
threads,  A  B,  the  one  within  the  other. 
One  turns  upward,  while  the  other  turns 
downward  with  a  little  greater  velocity, 
so  that  the  whole  screw  advances  in  pro- 
portion to  the  difference  between  the  larg- 
er and  smaller  threads.  This  difference 
may  be  very  small,  and  hence  the  power 
may  be  very  great ;  but  in  this,  as  in  all 
cases  where  great  power  is  generated  with 
a  sfight  force,  the  screw  moves  very  slowly,  so  that  the  force 
must  be  applied  for  a  long  time  to  exert  very  great  pressure. 

The  Micrometer  Screw  acts  on  the  above  principle,  and  is  much 
used  to  measure  very  small  distances,  particularly  where  very 
accurate  measurements  are  required.  In  order  to  understand 
this,  suppose  the  lever,  Fig.  80,  moves  over  a  graduated  arc  three 
inches  in  circumference,  divided  into  100  equal  parts,  and  that 
the  larger  screw,  A,  is  one  inch  in  length,  with  100  threads; 
the  smaller,  B,  of  the  same  length,  and  101  threads.  Now  one 
revolution  of  the  index  will  advance  the  screw  the  difference  be- 
tween T£o-th  and-  T¥Ttn  °f  an  mcn>  or  Too—  T^T  —  To-^oT  °f  an 

inch.     While  the  index,  therefore,  is  passing  one  division  Tfoth 


Upon  what  does  its  power  depend,  and  how  is  it  limited  ?    Describe  the 
principle  of  Hunter's  screw — the  micrometer  screw, 


THE    WEDGE.  109 

of  a  revolution,  the  screw  will  lengthen  only  T£o-th  of  TO-TO^^ 
T-OTF-O^O-  inches,  or  one  million  ten  thousandth  of  an  inch  ! 
spaces  so  small  as  to  require  a  powerful  microscope  to  distin- 
guish them. 

F!g.  £i.  Ill-  Wedge. — The  wedge,  Fig.  81,  is 

another  form  of  using  the  inclined  plane, 
for  the  purpose  of  cleaving  rocks  and  wood, 
for  raising  vessels,  &c.  All  instruments 
used  for  cutting  or  separating  bodies  into 
parts,  such  as  axes,  knives,  chisels,  awls,  &c.,  are  wedges. 

We  may  estimate  the  power  of  the  wedge  by  considering  one 
half  of  the  back  as  the  height  of  the  plane,  and  the  sides  its 
length.  If,  now,  the  wedge  be  driven  under  a  beam,  it  will 
raise  it,  and  the  power  requisite  to  do  this  will  be  to  the  weight 
of  the  beam  as  the  height  of  the  plane,  or  half  the  back  of  the 
wedge  to  its  length  :  P  :  W  :  :  c  e  :  c d;  .-.  Pxlength=Wx^ 
back ;  or,  the  power  equals  the  weight  multiplied  into  half  of 
the  back  and  divided  by  the  length. 

Unlike  all  the  other  mechanical  powers,  the  practical  use  of 
the  wedge  depends  upon  friction.  Were  the  friction  destroyed, 
it  could  be  of  no  service.  This  is  illustrated  in  attempting  to 
split  a  frozen  log.  The  wedge,  when  driven  in  by  a  stroke  of 
the  beetle,  as  there  is  little  friction,  is  forced  out  again  by  the 
elasticity  of  the  parts  which  are  separated. 

The  wedge  is  an  instrument  of  great  power,  and  is  much  used 
in  all  the  mechanical  arts. 

SECTION  III.— REGULATION  OF, MACHINERY  AND  MODIFICATION  OF  MO- 
TION.    FRICTION. 

I.  In  order  to  give  uniformity  to  the  'motion  of  machinery 
under  the  influence  of  varying  forces,  certain  contrivances  are 
resorted  to,  in  which  the' force  of  inertia  is  employed  to  accumu- 
late power,  and  to  apply  it  when  it  is  needed.      The  most  im- 
portant of  these  are  the  fly- wheel  and  the  governor. 

II.  To  change  the  direction  of  motion,  certain  other  contri- 
vances, are  employed,  as  cog-wheels  and  joints. 

Describe  the  wedge.  How  does  its  action  differ  from  other  mechanical 
powers  ? 


110  NATUilAL    PHILOSOPHY. 

III.  In  consequence  of  the  rubbing  of  the  parts  of  machinery 
there  arises  a  certain  amount  of  friction,  to  overcome  wliich  a 
force  must  be  applied,  the  intensity  of  which  will  depend  upon 
the  nature  of  the  surfaces  and  the  degree  of  p)-essure. 

I.  IN  consequence  of  the  inertia  of  matter,  and  of  the  fact  that 
this  inertia  is  overcome  by  any  force  gradually,  there  is  in  ma- 
chinery a  tendency  to  uniformity  of  motion  ;  hence, 

If  the  amount  of  matter  set  in  motion  is  very  large,  as  is  the 
case  in  large  mill-stones  or  a  steam  vessel,  any  sudden  increase 
or  diminution  of  force  will  but  slightly  affect  the  rate  of  motion  ; 
but  when  machinery  is  not  so  ponderous,  variations  of  power 
will  produce  variations  of  motion — sudden  jerks  or  impulses, 
which  not  only  diminish  the  utility  of  the  machine,  but  tend  to 
injure  or  destroy  it.  In  such  cases,  certain  contrivances  are  re- 
sorted to  for  the  purpose  of  rendering  the  motion  uniform,  under 
the  influence  of  varying  degrees  of  force. 

The  most  important  regulators  of  machinery  are  the  fly-wheel 
and  the  governor. 

1 .  Fly-wheel. — The  fly-wheel  is  simply  a  heavy  wheel  of  cast 
iron,  attached  to  the  revolving  parts  of  machinery  in  such  a  way 
as  to  be  put  in  motion,  and  thereby  to  accumulate  power.  If  the 
force  is  deficient  at  any  one  moment,  this  power  will  supply  it ;  if 
the  force  is  suddenly  increased,  the  fly  will  oppose  its  inertia  to  any 
sudden  impulse,  and  by  these  means  the  motion  is  rendered  uniform. 

This  accumulation  of  power  by  means  of  the  fly-wheel  is  of 
great  importance  in  the  printing  press  and  some  other  machines 
where  force  is  required  to  be  applied  by  successive  strokes. 

For  coining  metals  and  for  stamping  patterns,  where  great 
power  is  required,  a  different  kind  of  fly  is  used,  or,  rather,  the 
fly  is  made  to  act  upon  a  screw,  so  as  to  force  the  end  of  the 
screw,  which  is  connected  with  the  diet  against  the  object  which 
is  to  receive  the  stamp. 

A  great  variety  of  useful  and  ornamental  work,  such  as  fire- 

What  causes  operate  to  produce  uniformity  of  motion  ?  What  contrivan- 
ces are  resorted  to  to  render  motion  uniform  ?  Describe  the  action  of  the 
fly-wheel.  How  is  the  fly  employed  in  coining  and  stamping  metals  ? 


MODIFICATION    OF    MOTION. 


Ill 


fenders,  grates,  silver,  copper,  and  bronze  ware,  are  stamped  in 

this  way. 

2.  Governor. — The  governor  is  another  instrument  to  regulate 

motion,  especially  that  connected  with  steam  power. 

Fig.  82.  It  consists  of  two  heavy  balls,  Fig.  82,  which  are 
so  attached  to  an  axis  that,  when  revolution  takes 
place,  they  separate  more  or  less,  according  to  their 
velocity.  When  the  motion  becomes  too  rapid,  the 
balls  separate  so  far  as  to  close  a  valve  which  lets  the 
steam  into  the  piston,  and  this  checks  the  motion. 
As  the  motion  is  slower,  the  balls  fall  together,  open 
the  valve,  and  let  the  steam  in  again  to  increase  the 
motion. 

As  the  valve  is  opened  and  closed  gradually,  there 
is  a  gradual  increase  or  diminution  of  power,  and  the 
motion  of  the  machinery  is  thereby  rendered  uniform. 

II.  Modification  of  Motion. — It  is  often  desirable  to  change 
the  direction  of  motion  from  horizontal  to  vertical,  or  from  circu- 
lar to  reciprocating,  and  the  reverse.  For  this  purpose,  cog- 
wheels and  joints  are  employed,  called 

Gearing. — Cog-wheels  have  been  noticed  on  page  91,  where 
the  object  was  to  increase  or  diminish  velocity.  They  are  also 
used  to  change  the  direction  of  motion,  in  which  case  they  oc- 
cupy different  positions  in  reference  to  each  other,  or  else  the  di- 
rection in  which  the  teeth  are  cut  is  varied. 

1 .  If  the  teeth  lie  in  the  same  plane  with  the  wheels,  it  is  call- 
ed spur  gearing,  in  which  case  the  direction  of  the  motion  is  not 
changed. 

2.  If  the  teeth  are  cut  obliquely  to  the  axis,  it  is  called  spiral 
gearing. 

3.  If  the  wheels  are  situated  in  different  planes, 
and  are  shaped  like  the  frustra  of  cones,  Fig.  83, 
the  teeth  also  being  cut  obliquely,  so  as  to  give 
different  directions  to  motion,  varying  according 
to  the  angle  which  the  axes  of  the  wheels  make 
.with  each  other,  it  is  called  bevel  gearing. 

Describe  the  governor.     How  does  it  regulate  the  motion  of  the  steam- 
engine  1    What  are  the  contrivances  for  changing  the  direction  of  motion 1  • 
Describe  the  different  kinds  of  gearing. 


.83. 


112 


NATURAL    PHILOSOPHY. 


Fig.  84. 


If  the  teeth  are  so  cut  as  to  prevent  motion  in  one  direction  by 
means  of  a  catch,  while  it  allows  it  in  the  opposite  direction,  it 
is  called  a  ratchet  wheel. 

If  the  axis  of  motion  is  one  side  of  the  center  of  a  wheel,  so 
that  the  velocity  of  the  circumference  varies  at  different  points,  it 
is  called  an  eccentric  wheel.  Such  wheels  are  used  in  orreries, 
to  exhibit  the  varying  motions  of  the  planets  in  their  orbits. 

Reciprocating  Motion  is  generally  produced  by  means  of  a 
crank  attached  to  a  wheel  with  a  shaft,  which  rises  up  and  down 
as  the  wheel  turns.  This  is  exemplified  in  the 
saw-mill,  steam-engine,  and  some  other  rna- 
chines. 

The  arch  head  is  also  used  for  reciprocating 
motion.  It  consists  of  an  arc  on  the  end  of  a 
lever,  Fig.  84,  moving  upon  a  pivot,  C.  Some- 
times a  chain,  P  B,  is  laid  upon  the  arc  B  D, 
so  that,  as  the  lever  wrorks  back  and  forth,  a 
vertical  motion  is  given  to  a  rod  attached  to  P. 
This  is  often  the  arrangement  in  the  lifting- 
pump.  Sometimes  teeth  are  cut  in  the  arc  B  D, 
so  as  to  act  on  rack-ivork. 

The  knee  joint  is  a  mechanical  power  used  in 
the  printing-press.  It  consists  of  two  levers, 
Fig.  85,  united  by  a  joint,  a,  with  the  end  of 
one  firmly  secured,  and  that  of  the  other  con- 
nected with  a  movable  block.  The  joint,  a,  on 
being  forced  in,  causes  the  levers  to  press  down 
upon  the  block  with  a  force  which  increases 
rapidly  as  they  approach  a  straight  line.  By 
this  means  a  very  great  pressure  may  be  exerted 
with  but  slight  additions  of  power. 

The  universal  joint,  Fig.  86,  consists  of  two 
semicircular  arcs  connected  by  cross  pieces,  upon 
which  the  arcs  may  turn  in  every  direction. 
Sometimes  a  ball  is  made  to  turn  in  a  socket,  so 
as  to  give  a  free  motion.  In  surveyor's  compass- 
es and  some  other  instruments  this  kind  of  joint 
is  employed. 

How  does  the  ratchet  wheel  operate  ?  How  is  the  eccentric  wheel  con- 
structed ?  How  is  reciprocating  motion  produced  1  Describe  the  arch 
head.  Describe  the  knee  joint — the  universal  joint. 


Fig.  85. 


Fig. 


ROLLING    AND    SLIDING    FRICTION.  113 

III.  Friction. — In  treating  of  the  mechanical  powers,  we  have 
regarded  them  as  destitute  of  friction,  simply  alluding  to  the  al- 
lowance which  must  be  made  for  it.  There  is  a  certain  force  re- 
quired to  overcome  friction  produced  by  the  rubbing  of  the  parts 
upon  each  other,  and  upon  surfaces  in  contact  with  the  machine. 

Friction  arises  from  the  elevations  of  one  surface  falling  into 
the  depressions  of  another.  The  following  diagram  will  illus- 
trate the  manner  in  which  such  resistance  to  motion  takes  place. 

The  body  a,  Fig.  87,  in  order  to  be  Fig.&t. 

dragged  across  c  b,  must  be  lifted  over 
the  proj ecting  points.  All  surfaces,  how- 
ever smooth  they  may  appear  to  be,  have 
elevations  and  depressions,  and  to  over- 
come the  friction  thus  produced,  a  cer- 
tain force,  varying  for  different  surfaces 
and  substances,  must  be  expended. 

This  force  can  only  be  determined  by  experiment. 

Thus  it  is  found  by  experiment  that  it  requires  27 '7  Ibs.  to 
overcome  the  friction  of  100  Ibs.  of  iron,  moving  on  a  horizontal 
layer  of  iron :  hence  its  coefficient  of  friction  is  0- 27 -7,  or  27*7  per 
cent. 

The  mode  of  determining  the  amount  of  friction  is  to  place  a 
block,  as  of  oak,  of  a  given  weight,  upon  a  horizontal  surface  of 
oak,  and  ascertaining  the  force  necessary  to  move  it  over  the 
surface. 

The  ratio  which  this  bears  to  the  weight  of  the  block  is  called 
the  coefficient  of  friction. 

It  is  thus  found  that  the 

coefficient  of  iron  upon  iron  is  0-277 
"  "  iron  upon  brass  is  0-263 
"  "  iron  upon  copper  is  0-170 

"  "  oak  upon  oak  is         0-418 

"  "  oak  upon  pine  is        0-667 

"  pine  upon  pine  is      4-562. — MU'LLKR. 

Where  the  experiment  is  tried  with  wood,  the  coefficient  of 
friction  will  be  greater  when  the  motion  is  across  the  grain  than 
when  it  is  in  the  same  direction  with  the  fiber. 

How  does  the  friction  of  machinery  arise  ?  How  is  the.  force  of  friction 
determined  ?  What  is  the  coefficient  of  friction  ? 


114  NATURAL    PHILOSOPHY. 

In  all  these  cases  the  friction  is  directly  proportioned  to  the 
weight  of  the  block,  and  not  to  the  extent  of  sur/ace.  If  a  block 
have  two  square  feet  on  one  side  and  one  on  the  other,  it  will 
make  no  difference  which  side  is  applied  to  the  horizontal  sur- 
face, the  friction  will  be  the  same. 

This  is  called  sliding  friction,  and  may  be  diminished  by  oil- 
ing the  surfaces.  Oil  is  the  best  for  metals,  but  tallow  for  wood. 

Sliding  friction  occurs  at  the  point  where  axles  revolve  in  their 
supports,  as  in  the  case  of  common  wheels.  The  amount  is  de- 
termined by  experiment,  and  obviated,  in  part,  by  keeping  the 
axles  well  oiled. 

Rolling  friction  is  the  resistance  which  a  round  body  meets 
with  in  rolhng  along  a  level  surface.  This  kind  of  friction  is 
much  less  than  sliding  friction.  The  amount  may  be  determined 
in  the  same  way. 

In  the  wheels  of  carriages,  there  is  sliding  friction  at  the  axles 
and  rolling  friction  at  the  circumferences,  both  of  which  are  di- 
minished as  the  wheels  increase  in  size. 

The  driving  wheels  of  a  locomotive,  as  they  are  turned  by  the 
force  of  steam,  propel  the  whole  carriage,  with  twenty  or  thirty 
heavy  cars  in  connection,  because  the  rolling  friction  of  all  the 
wheels,  together  with  the  sliding  friction  of  all  the  axles,  is  less 
than  the  sliding  friction  between  the  wheel  and  the  rail. 

When  the  rolling  friction  of  all  the  attached  cars  becomes  equal 
to  the  sliding  friction  between  the  propelling  wheels  and  the  iron 
rail,  the  propelling  wheels  will  revolve  without  moving  the  load. 
This  often  takes  place  when  the  track  is  wet,  covered  with  ice, 
or  frozen.  We  may  then  notice  rapid  revolutions  of  the  propelling 
wheels,  especially  when  the  train  attempts  to  start.  Hence  it 
appears,  that  the  weight  of  the  locomotive,  which  increases  the 
sliding  friction,  is  as  much  concerned  in  moving  heavy  loads  as 
the  power  of  its  engine. 

Strength  of  Materials. — It  is  an  important  problem  in  all 
mechanical  structures  to  determine  the  strength  of  the  materials 

To  what  is  friction  proportioned?  Describe  sliding  friction.  What  is 
rolling  friction?  What  kind  of  friction  in  wheel  carriages?  Why  do  the 
propelling  wheels  of  the  locomotive  sometimes  revolve  without  moving  the 
train? 


STRENGTH    OF    MATERIALS.  115 

employed,  and  then  so  to  arrange  them  as  to  give  to  the  struc- 
ture the  greatest  strength  of  which  the  materials  are  capable. 
The  strength  of  materials  is  estimated  in  different  directions. 

1.  The  resistance  which  a  bar  or  wire  of  any  substance  op- 
poses to  a  force  which  tends  to  part  it  in  the  direction  of  the 
length,  is  called  the  ABSOLUTE  strength. 

This  is  determined  by  fastening  one  end,  and  applying  weights 
to  the  other  till  it  is  parted  or  drawn  asunder. 

If  several  metallic  wires  of  the  same  diameter  are  fastened  by 
their  ends,  and  weights  applied,  iron,  in  the  form  of  steel,  will  be 
found  to  have  the  greatest  tenacity.  A  steel  bar  of  one  inch 
square  will  sustain  135,000  Ibs.,  a  gold  bar  of  the  same  size  will 
sustain  but  22,000  Ibs.,  while  a  similar  lead  bar  will  part  with 
a  weight  of  only  800  Ibs.  The  strength  of  wire  is  increased  by 
drawing  it  out,  as  there  is  given  to  the  atoms  of  the  surface 
greater  tenacity  than  to  the  atoms  within  the  wire,  so  that  if  the 
surface  of  a  wire  be  removed  by  a  piece  of  sand  paper,  its  strength 
will  be  much  diminished  ;  hence,  by  twisting  many  wires  to- 
gether and  increasing  the  surface,  the  strength  of  the  metal  is 
much  greater  than  when  it  is  in  one  solid  wire.  Some  of  the 
heaviest  bridges  are  sustained  by  iron  cables  made  of  small  wire. 
The  same  is  true  of  hemp  and  silk  cords ;  the  latter  possesses 
twice  the  strength  of  the  former ;  and  their  tenacity  is  still  fur- 
ther increased  by  gluing  the  threads  together.  By  wetting  the 
cord  it  is  also  rendered  stronger. 

2.  The  resistance  which  a  body  opposes  to  a  force  applied  di- 
rectly across  it,  when  one  or  both  ends  are  supported,  is  called  the 
LATERAL  strength. 

This  is  generally  much  less  than  the  absolute  strength.  The 
strength  of  a  beam,  supported  at  the  two  ends,  and  weights  applied 
at  the  center,  will  depend,  1st,  upon  its  length ;  the  shorter  it  is, 
the  greater  its  power  of  resistance ;  2d,  upon  its  breadth  and 
depth,  the  strength  being  as  the  breadth  multiplied  into  the 
square  of  the  depth ;  hence  a  board  will  be  strongest  when  placed 

How  is  the  strength  of  materials  estimated  ?  What  is  absolute  strength, 
and  how  is  it  determined  ?  Of  the  metals  which  is  the  most  tenacious  ? 
What  influence  has  the  twisting  of  the  fiber  upon  the  strength?  What  is 
the  lateral  strength  of  material  ? 


116  NATURAL    PHILOSOPHY. 

on  its  edge.     If  the  beam  is  supported  at  one  end,  its  strength  is 
but  about  one  fourth  as  great. 

3.  The  resistance  to  compression  increases  with  the  thickness 
of  the  body  until  it  has  reached  a  certain  diameter,  and  then  di- 
minishes.    In  this  case  the  pressure  may  be  made  directly  across 
the  body,  as  is  the  case  with  a  wedge,  or  lengthwise,  as  is  illus- 
trated by  pillars  that  sustain  heavy  structures. 

4.  The  resistance  which  a  body  opposes  to  being  twisted  is 
called  the  strength  of  torsion.     This  power  varies  very  much, 
arid  depends  upon  elasticity.      Some  bodies  may  be  twisted  to  a 
great  extent  and  return  again  to  their  former  position,  while 
others  are  easily  broken  by  twisting  them,  or  become  permanent- 
ly bent.     These  points  are  the  limits  of  the  force  of  torsion. 

In  the  arrangement  of  materials  to  form  any  structure,  as  a 
bridge,  the  form  of  the  arch  gives  the  greatest  strength,  because 
\he  weight  is  more  equally  distributed  through  all  the  materials 
which  compose  the  structure.  In  the  case  of  beams  they  should 
be  much  deeper  than  broad,  and  if  inclined  at  an  angle  will  bear 
a  greater  strain  than  when  laid  horizontally.  The  strength  of  a 
beam  may  be  increased  by  making  it  of  several  pieces,  one  laid 
upon  the  other,  or  side  by  side,  and  fastened  together.  Circular 
beams  may  be  made  stronger  with  the  same  weight,  and  even 
with  a  less  weight,  by  making  them  hollow. 

In  estimating  the  strength  of  materials  and  in  their  arrange- 
ment, allowance  must  be  made  for  their  own  weight  as  well  as 
the  weight  they  are  intended  to  sustain.  It  sometimes  happens 
that  a  structure  will  be  very  strong  when  a  small  model  only  is 
tried,  but  when  it  is  applied  on  a  larger  scale  it  will  be  crushed 
by  its  own  weight.  The  structure  and  size  of  animals  and  of 
plants  bear  a  constant  relation  to  the  strength  of  the  material  of 
which  they  are  composed.  The  bones  of  birds  are  hollow.  The 
limbs  of  animals,  from  the  smaller  to  the  larger,  increase  in 
breadth  more  than  in  length  or  height. 

Practical  Utility  of  the  Medianical  Powers. — In  treating  of 
the  mechanical  powers,  we  have  frequently  repeated  the  fact,  that 

What  the  resistance  to  compression  ?  How  is  the  strength  of  torsion  esti- 
mated ?  What  arrangement  of  material  offers  the  greatest  resistance  ? 


..xILITY    OF    THE    MECHANICAL    POWERS.  117 

there  is  no  mechanical  advantage  in  their  use,  on  the  broad  prin- 
ciple tlwt  ivliat  is  gained  in  power  is  lost  in  time.  This  is  the- 
oretically, but  not  always  practically  true. 

1 .  For,  even  when  muscular  power  alone  is  applied,  there  is 
practically  a  very  great  advantage  in  their  use.     Take,  for  ex- 
ample, the  pulley.     In  theory,  if  one  man,  by  means  of  the  pul- 
ley, is  able  to  raise  a  block  200  feet  which  would  require  the 
strength  of  five  men  to  raise  it  through  the  same  space,  it  will 
take  him  five  times  as  long  to  do  it.     But  when  we  come  to  ap- 
ply this  theory  in  practice,  we  often  find  that  one  man,  by  means 
of  the  pulley,  will  actually  raise  a  weight  200  feet  which  five  men 
without  mechanical  aid  would  be  unable  to  raise  at  all ;  for,  al- 
though they  may  be  able  to  exert  five  times  the  force,  yet  they 
may  not  be  able  to  expend  that  force  upon  the  block  in  such  a 
way  as  to  raise  it  to  the  required  position.     The  same  is  true  in 
the  use  of  the  lever.     Where  a  heavy  weight  is  to  be  raised  a 
small  distance,  one  man  may  exert  the  force  of  five  men,  and 
actually  raise  the  weight  in  less  time  than  it  could  be  done  by 
the  direct  muscular  effort  of  the  five. 

The  same  may  be  true  in  the  use  of  all  the  mechanical  pow- 
ers. It  is  emphatically  true  in  relation  to  the  screw  and  wedge, 
in  cases  where  the  strength  of  numbers  can  not  be  applied.  We 
know  that  a  single  individual,  by  means  of  the  wedge,  is  able  to 
split  open  rocks  and  blocks  of  wood  which  the  strength  of  5000 
men  could  not  accomplish  by  the  mere  exertion  of  muscular 
power. 

It  should  be  observed  further,  that  even  if  |he  force  of  num- 
bers could  be  as  readily  applied  as  that  of  one,  there  is  a  special 
advantage  in  the  use  of  the  lever  and  pulley,  in  consequence  of 
the  direction  in  which  the  force  is  generally  applied;  for  we 
make  use  of  the  gravity  or  iveight  of  the  body,  in  connection  with 
its  muscular  power,  to  raise  weights  in  opposition  to  gravity. 

2.  But  the  utility  of  the  mechanical  powers  is  more  strikingly 
illustrated  in  cases  where  natural  forces,  as  those  of  water,  air, 
and  steam,  are  applied  to  impart  motion  to  machinery.     In  such 

Mention  the  practical  uses  of  the  mechanical  powers.  Upon  what  do 
the  useful  results  of  water  and  steam  power  depend? 


118  NATURAL    PHILOSOPHY. 

cases,  the  doctrine  -that  "what  is  gained  in  power  by  the  mech- 
anism is  lost  in  time"  has  no  practical  application,  for  it  is  at 
once  obvious  that  the  running  of  water,  the  motion  of  air,  and 
the  expansive  force  of  steam,  depend  wholly,  for  any  useful  result, 
upon  the  machinery  by  which  their  power  is  directed  and  applied. 

By  the  application  of  steam  and  water  to  various  combina- 
tions of  the  mechanical  powers,  we  are  enabled  to  accomplish 
that  which  no  unaided  human  effort  is  able  to  achieve ;  and  not 
only  so, 

But  there  is  in  the  use  of  mechanism  greater  perfection,  great- 
er economy,  and  saving  of  time  and  expense  in  respect  to  those 
products  of  art  in  the  production  of  which  both  muscular  and 
mechanical  forces  are  employed.  The  whole  circle  of  the  me- 
chanical arts,  from  the  steam-ship  to  the  pin  factory,  is  filled  with 
illustrations  of  their  great  utility  to  civilized  man. 

"Practical  Mechanics,"  says  Herschel,  "is,  in  the  most  pre- 
eminent sense,  a  scientific  art,  and  it  may  be  truly  asserted  that 
almost  all  the  great  combinations  of  modern  mechanism,  and 
many  of  its  refinements  and  nicer  improvements,  are  creations  of 
pure  intellect,  grounding  its  exertion  upon  a  moderate  number 
of  very  elementary  propositions  in  Theoretical  MecJianics  and  Ge- 
ometry. On  this  head  we  might  dwell  long,  and  find  ample 
matter  both  for  reflection  and  wonder  ;  but  it  would  require,  not 
volumes  merely,  but  libraries,  to  enumerate  and  describe  the 
prodigies  of  ingenuity  which  have  been  lavished  on  every  thing 
connected  with  machinery  and  engineering.  By  these  it  is  that 
we  are  enabled  to  diffuse  over  the  whole  earth  the  productions 
of  any  part  of  it ;  to  fill  every  corner  of  it  with  miracles  of  art 
and  labor  in  exchange  for  its  peculiar  commodities,  and  to  con- 
centrate around  us,  in  our  dwellings,  apparel,  and  utensils,  the 
skill  and  workmanship,  not  of  a  few  expert  individuals,  but  of  all 
who  in  the  present  and  past  generations  have  contributed  their 
improvements  to  the  processes  of  our  manufactures." 

3.  The  utility  of  the  mechanical  powers  may  indeed  be  viewed 
from  a  higher  position.  They  have  furnished  the  human  intel- 

What  special  advantage  in  the  use  of  machinery  ?  From  what  higher 
point  may  we  view  the  mechanical  powers  ? 


HYDRODYNAMICS.  119 

lect  with  an  opportunity  for  achieving  some  of  its  highest  tri- 
umphs. They  have  enabled  it  to  penetrate  into  the  mysteries  of 
the  universe,  and  to  gain  a  more  enlarged  and  clearer  view  of 
the  plans  and  purposes  of  the  Creator. 


CHAPTER  IV. 

HYDRODYNAMICS. 

HYDRODYNAMICS*  is  that  branch  of  science  which  treats  of  the 
Mechanical  Properties  of  Liquids.  It  is  divided  into  Hydrostat- 
ics and  Hydraulics. 

Hydrostatics  is  a  term  derived  from  two  Greek  words,  and 
means  Water-statics.  As  a  branch  of  Natural  Philosophy,  it 
treats  of  the  equilibrium  and  pressure  of  liquids. 

Hydraulics  treats  of  the  motion  of  liquids,  and  the  effects  of 
their  motion. 

Liquids  differ  from  solids  in  the  circumstance  that  their  par- 
ticles move  freely  upon  each  other.  They  differ  from  gases  and 
vapors  in  the  fact  that  it  requires  much  greater  force  to  compress 
them,  and  hence  they  have  been  called  non-elastic  fluids,  while 
gases  and  vapors  have  been  termed  elastic  fluids. 

There  are  slight  grounds,  however,  for  this  distinction.  Li- 
quids are  elastic  fluids.  According  to  the  experiments  of  Mr. 
Perkins,  a  pressure  of  30,000  Ibs.  to  the  square  inch  causes  a 
mass  of  water  to  contract  one  twelfth  of  its  volume,  and  the  vol- 
ume is  restored  when  the  pressure  is  removed. 

SECTION  I.— HYDROSTATICS. 

Liquids  differ  from  solids  in  the  fact  that  their  atoms  are  less 
under  the  influence  of  cohesion,  and  hence  Imve  a  freer  motion 

*  The  term  hydrodynamics  is  sometimes  used  in  the  same  sense  as  hy- 
draulics. It  jaeans  water-dynamics,  but  may  appropriately  be  used  in  a 
more  generic  sense ;  for  water  at  rest,  as  well  as  in  motion,  exerts  a  con- 
stant force,  which  is  due  to  its  gravity. 

What  is  the  meaning  of: hydrostatics  and  of  hydraulics  1  Of  what  do  they 
treat  T 


120 


NATURAL    PHILOSOPHY. 


among  themselves,  in  conseque^e  of  which  the  force  of  gravity 
draws  each  atom  separately  toward  the  center  of  the  earth;  hence 

I.  The  pressure  of  any  liquid  contained  in  a  vessel  is  equal 
in  all  directions,  downward,  upward,  and  laterally. 

II.  The  amount  of  pressure  of  any  liquid  contained  in  a  ves- 
sel is  equal  to  a  column  whose  base  is  the  area  of  the  lottoin,  and 
whose  height  is  equal  to  the  depth  of  the  liquid,  whatever  be  the 
form  or  size  of  the  vessel. 

III.  It  results  from  the  laws  of  pressure  that  liquids  will  rise 
to  the  same  height  in  tubes  connected  with  a  common  reservoir, 
whatever  their  form  or  capacity;  and  also  that  the  surface  of  a 
liquid  at  rest  is  always  level. 

IV.  A  body  immersed  in  any  liquid  loses  a  portion  of  its 
weight  equal  to  the  weight  of  the  liquid  displaced,  and  hence  by 
weighing  bodies  in  air  and  then  in  water,  their  relative  weights 
or  specific  gravities  may  be  determined. 

V.  Bodies  lighter  than  liquids  will  float  upon  tJieir  surfaces, 
and  displace  a  quantity  of  liquid  equal  to  their  own  weight. 

LIQUIDS  as  well  as  solids  are  under  the  influence  of  gravity, 
but,  in  consequence  of  the  freedom  of  motion  among  their  atoms, 
each  atom  of  a  mass  is  separately  attracted  toward  the  center  of 
the  earth.  T^Q  fundamental  difference  between  a  liquid  and  a 
solid  in  this  respect  depends  upon  the  relative  force  of  cohesion 
and  gravity* 

This  distinction  may  be  il- 
lustrated by  the  opposite  dia- 
gram : 

Let  a  b,  Fig.  88,  be  two 
atoms  of  a  solid,  e  d  two  sim- 
ilar atoms  of  any  liquid,  a  e 
b  /the  'direction  of  the  force 

*  Liquids  have  an  attraction  for  solids,  which  is  manifested  in  the  case 
of  capillary  tubes,  called  capillary  attraction  (see  page  32).  There  are 
many  phenomena  of  liquids  which  are  explained  by  reference  to  this  force. 
All  porous  bodies  .will  absorb  water.  The  wick  of  a  lamp  consists  of  a 
series  of  capillary  tubes,  which  draw  up  the  oil  to  supply  the  flame.  A 
cloth  with  one  end  dipped  into  a  basin  of  water  will  empty  the  vessel,  &c. 

How  do  liquids  differ  from  solids  ?     Illustrate  the  distinction. 


Fig.  88. 


B 


PRESSURE    OF    LICIUID3.  121 

of  gravity,  a  b  of  cohesion.  Now,  as  the  cohesive  force  in  a  b  is 
greater  than  that  of  gravity,  the  two  atoms  will  have  a  common 
center  of  gravity  at  n,  and  if  that  point  is  sustained  the  two  atoms 
will  be ;  but  as  the  force  of  cohesion  in  the  two  atoms  of  the 
liquid,  e  d,  is  less  than  gravity,  if  their  common  center,  c,  is  sus- 
tained, they  will  separate  and  fall. 

If  now  a  third  atom  be  added  to  each,  £,  g,  the  three  atoms 
of  the  solid  will  still  have  a  common  cen- 
ter of  gravity  ;  but,  on  adding  the  third 
atom  to  the  liquid,  it  will  press  between 
the  other  two,  force  them  apart,  and  the 
three  atoms  will  arrange  themselves  at 
the  same  distance  from  the  center  of  the 
earth,  as  in  e  g  d,  Fig.  89. 
It  will  be  seen,  that  while  the  solid  presses  downward  only, 
the  liquid  presses  in  a  lateral  direction  ;  and  if  there  are  a  series 
of  atoms,  those  below  must  sustain  those  above,  and  hence  an  up- 
ward pressure.  From  this  peculiar  property  of  the  atoms  of  a 
liquid,  each  being  free  to  move  in  all  directions,  influenced  by  its 
own  proper  gravity  in  a  manner  independent  of  all  the  rest,  we 
derive  the  fundamental  proposition  of  hydrostatics  : 

I.  The  pressure  of  a  liquid  contained  in  any  vessel  is  equal 
in  all  directions,  downward,  upivard,  and  laterally. 

1.  Doivnivard  Presswe.  —  That  liquids  have  a  downward 
pressure  is  too  evident  to  need  illustration.     It  results  directly 
from  gravity.     It  is  also  evident  that  each  stratum,  from  the  top 
to  the  bottom  of  the  vessel,  must  add  its  own  weight  to  the  next 
below  it,  until  the  whole  downward  pressure  rests  on  the  bottom 
of  the  vessel. 

2.  Lateral  Pressure  of  Liquids. — Liquids  press  later  ally  with 
the  same  force  that  they  press  downward. 

Fig.  90.  This  fact  is  not  so  obvious  as  the  preceding,  and 
yet  it  results  directly  from  it,  and  from  the  absence 
of  cohesion  among  the  atoms.  Thus,  suppose  a  c, 
Fig.  90,  represent  two  atoms  of  any  liquid,  so  plac- 
ed in  a  vessel  that  they  shall  touch  the  sides  and 
bottom.  If  a  third  atom,  b,  is  placed  between  them, 
it  will  tend  to  press  them  asunder,  and  must  cause  a  lateral  force 
to  be  exerted  upon  the  sides  of  the  vessel. 

What  is  the  fundamental  proposition  in  hydrostatics?     What  evidence 
of  downward  pressure  ?     How  is  the  lateral  pressure  of  liquids  proved  ? 


122 


NATURAL    PHILOSOPHY. 


That  the  lateral  pressure  is  equal  to  the  doivmvard 
pressure  may  be  proved  by  experiment.  Thus  : 

Exp. — If  an  aperture  be  opened  in  the  side  of  a  vessel  con- 
taining water,  Fig.  91,  on  a  level  with  the  bottom,  and  one  of 
the  same  size  in  the  bottom,  the  two  streams  will  issue  with 
the  same  velocity,  and  discharge  the  same  quantity  of  water 
during  any  given  time. 

3.  Upward  Pressure. — Liquids  press  upward  with 
the  same  force  that  they  press  downward  and  laterally. 

The  upward  pressure  of  a  liquid  is  due  directly  to  its  down- 
ward pressure,  on  the  principle  that  action  and  reaction  are  equal, 
and  in  opposite  directions.  If  one  stratum  of  a  mass,  1  {Fig.  91), 
press  downward  with  a  force  of  one  pound  upon  a  second  stratum, 
2,  then  this  second  stratum  must  press  upward  with  an  equal 
force,  or  it  could  not  sustain  it.  The  same  must  be  true  of  each 
stratum,  3,4,  &c.,  to  the  bottom  of  the  vessel. 

This  may  be  shown  more  clearly  by  the  following   . 

Exp. — Take  a  piece  of  glass,  a,  Fig.  9U,  with  a  string,  d,  at- 
tached to  its  center,  and  place  it  over  the  end  of  a  glass  tube,  b, 
open  at  both  ends.  Immerse  the  tube  in  a  vessel  of  water,  <?, 
and  the  upward  pressure  against  the  glass,  a,  will  be  such  that  it 
will  be  held  in  its  place  without  the  aid  of  the  string;  but,  oa 
taking  the  tube  out  of  the  water,  the  glass  will  full.  C 

All  floating  bodies  are  sustained  by  the  upward  press- 
ure of  the  liquid  ;  tor,  if  they  were  not,  they  would  neces- 
sarily sink  to  the  bottom  ;  and  the  reason  why  some  bodies  sink 
in  water,  while  others  float  upon  it,  is,  that  the  upward  pressure 
is  less  than  their  weight  in  the  former,  and  greater  than  their 
weight  in  the  latter  instance. 

II.  Amount  of  Pressure. — Having  shown  that  liquids  press 
equally  in  all  directions,  we  are  now  prepared  to  ascertain  the 
amount  of  this  pressure,  and  the  effects  of  it. 

The  amount  of  the  downward  pressure  of  any  liquid  con- 
tained in  a  vessel  is  equal  to  a  column  ivhose  base  is  the  sur- 
face of  the  bottom,  and  ivhose  height  is  equal  to  that  of  the 
liquid,  ivhatever  be  the  form  of  the  vessel.  In  case  the  vessel  is  of 
uniform  size,  as  a  cylinder,  it  is  evident  that  the  downward  press- 
To  what  is  it  equal?  What  proof  is  there  of  the  upward  pressure  of 
liquids  ?  How  are  floating  bodies  sustained  ?  What  is  the  amount  of  the 
pressure  of  any  liquid  equal  to  ? 


PRESSURE    OF    LiaUIDS. 


123 


Fig.  93. 


ure  will  equal  the  area  of  the  base  multiplied  into  its  height. 
As  the  sides  are  vertical,  and  can  not,  therefore,  sustain  any  part 
of  the  downward  pressure,  it  will  be  just  equal  to  the  weight  of 

the  liquid ;  but  if  the  sides  are  in- 
clined, as  in  Fig.  93,  then,  the 
weight  or  quantity  of  liquid  being 
the  same  as  before,  the  sides  will 
sustain  a  portion  of  the  weight,  so 
that  the  pressure  on  the  bottom,  C 
D,  will  only  be  equal  to  its  surface 
multiplied  into  its  perpendicular 
height  A  C,  and  hence  the  pressure 
on  the  bottom  will  be  less  than  the 
weight  of  the  liquid  in  the  vessel. 

But  in  Fig.  94,  as  the  pressure 
must  be  equal  over  the  whole  sur- 
face of  the  bottom,  E  F,  the  whole 
pressure  on  the  bottom  will  be  equal 
to  its  area  multiplied  into  the  verti- 
cal height  A  C,  and  will  therefore 
be  greater  than  the  weight  of  the 
liquid. 

Hence  the  pressure  on  a  given  surface  of  the  bottom  of  a  ves- 
sel will  be  as  its  height,  without  regard  to  inform  of  the  vessel, 
or  the  quantity  of  liquid  it  may  contain. 

Now  a  cubic  foot  of  water  weighs  62^  Ibs.  We  may  there- 
fore estimate  the  exact  force  of  pressure  on  the  bottom  and  sides 
of  rivers  and  upon  dams.  Thus,  if  the  water  is  eight  feet  deep, 
the  pressure  on  each  square  foot  will  be  500  Ibs. ;  if  forty  feet 
deep,  2500  Ibs. ;  and  if  it  is  one  mile  in  depth,  or  5280  feet,  the 
pressure  will  be  330,000  Ibs.  Hence  the  difficulty  of  confining 
a  high  column  of  water  in  pipes. 

It  is  owing  to  this  great  pressure  that,  in  the  construction  of 
dams  and  of  flood-gates,  it  is  necessary  to  make  the  parts  near  the 
bottom  stronger  in  proportion  as  the  depth  is  greater. 

Hence,  also,  the  difficulty  of  sounding  the  depth  of  the  ocean  ; 
for  the  water,  by  its  own  weight,  is  compressed,  at  the  depth  of 

What  influence  has  the  form  of  the  vessel  ?  How  does  the  pressure  of 
liquids  vary  ?  How  can  the  pressure  of  water  in  the  ocean  be  ascer- 
tained ? 


124 


NATURAL    PHILOSOPHY. 


Fig.  95. 


one  mile,  about  j-^th  of  its  volume.*  This  increase  of  density 
renders  it  difficult  to  sink  bodies  which  are  but  a  little  heavier 
than  water  to  very  great  depths.  Porous  bodies,  such  as  wood,  at 
the  depth  of  a  few  hundred  feet  become  compressed  by  this  force, 
and,  as  in  the  case  of  wrecked  vessels,  never  rise  to  the  surface. 

The  pressure  of  water  at  moderate  depths  is  proved  by  letting 
down  an  empty  bottle.  At  a  certain  depth  the  cork  will  be 
driven  in,  and,  even  if  the  bottle  is  filled  with  water,  the  salt 
water  will  be  forced  through  the  cork  and  mingled  with  that  in 
the  bottle. 

This  remarkable  law,  that  the  press- 
ure is  as  the  height,  may  be  proved  ex- 
perimentally by  an  apparatus,  Fig.  95, 
called 

The  Hydrostatic  Bellows.  —  This 
consists  of  an  India  rubber  bag,  D, 
which  may  be  filled  with  water  from 
cubes  of  different  forms  and  capacity, 
A  B  C  E,  but  of  the  same  length.  As 
the  bag  is  filled,  it  expands,  and  lifts 
weights  suspended  from  flat  boards  laid 
upon  the  top,  and  turning  on  hinges. 

If  the  tube  A  be  screwed  on  to  the 
bellows,  and  filled  with  water  until  it 
will  raise  a  weight  of  40  Ibs.,  and  then 
if  the  tubes  B  and  C,  each  in  turn,  are 
attached,  and  filled  to  the  same  height, 
it  will  be  found  that  each  will  exert  a 
pressure  just  equal  to  40  Ibs. 

The  quantity  of  liquid  in  A  may  be  10,50,  or  lO'OOO  times 
that  in  C,  and  still  the  force  of  pressure  upon  D  will  be  the  same 
in  all.  Hence,  by  increasing  the  height  of  the  column,  however 
small  the  tube  may  be,  the  pressure  will  be  increased  in  the  ra- 
tio of  the  heiht.  If  the  surface  of  the  bellows  be  increased,  the 


.  , 

*  Water  is  diminished  ^  J7-0th  of  its  volume  for  each  atmosphere  of  pr 
e  upon  it,  or  for  every  15  Ibs.  to  the  square  inch  ;  alcohol,  yy^rifth  o 
. 


ure  upon 
volume. 


ress- 
of its 


What  practical  use  should  be  made  of  the  pressure  of  liquids?  Why 
>an  not  the  ocean  be  sounded  to  its  bottom  ?  Describe  the  hydrostatic 
»ellowsf 


HYDROSTATIC    PARADOX.  125 

pressure  will  be  increased,  the  height  remaining  the  same.  If, 
therefore,  the  surface  of  the  bottom  be  made  very  large  and  the 
tube  very  high,  the  pressure  will  be  increased  in  a  compound  ra- 
tio. This  is  called  the 

Hydrostatic  paradox,  because  a  very  small  quantity  of  liquid 
may  be  so  applied  as  to  raise  a  very  large  weight.  A  single  pound 
of  water  may  be  made  to  exert  a  pressure  of  10,  50,  or  a  1000 
Ibs.  This  force  is  limited  only  by  that  of  capillary  attraction. 

The  precise  manner  in  which  this  is  effected  may  be  illustrated 
by  the  following  diagram  : 

Let  the  box  a  b,  Fig.  96,  be  three 
feet  square  and  one  foot  high.  It  will 
contain  nine  cubic  feet.  Let  the  tube 
1  2  3  be  one  foot  square  and  three 
feet  high. 

If  the  box  is  filled  with  water,  it 
will  press  upon  its  bottom  with  a 
force  of  62^  Ibs.  upon  each  square 
foot.  Pour  into  the  tube  62£  Ibs.  of 
water,  and  it  will  fill  the  tube  to  1, 
which  will  double  the  pressure  upon  the  base  of  the  column  im- 
mediately below  the  tube ;  but  the  lateral  pressure  upon  d,  and 
the  upward  pressure  upon  a,  must  each  be  equal  to  the  down- 
ward pressure,  and  the  same  must  be  true  at  e  and  b,  and  upon 
every  square  foot  of  the  inner  surface  of  the  box.  Hence  the 
weight  of  62^  Ibs.  of  water  will  increase  the  pressure  nine  times 
62^  Ibs.  upon  the  bottom,  nine  times  62|  Ibs.  upon  the  top,  and 
twelve  times  621  Ibs.  upon  the  four  sides  ;  or  the  whole  pressure 
upon  the  inner  surfaces  of  the  box  will  be  1875  Ibs.  If  the  tube 
be  filled,  or  twice  62£  Ibs.  of  water  be  added,  the  pressure  will 
be  twice  as  great.  If  now  the  tube  be  but  one  half  the  capac- 
ity, then  it  will  require  but  half  as  much  water  to  fill  it,  and 
yet  it  will  exert  the  same  pressure.  The  tube  might  be  dimin- 
ished in  size  until  the  force  of  capillary  attraction  (see  p.  32)  be- 
gan to  overcome  the  pressure,  and  three  feet  of  height  would  ex- 
ert the  same  force  upon  the  interior  of  the  box.  There  is  a  limit, 
therefore,  to  the  increase  of  pressure  ;  for  the  tube  may  become 
so  small  that,  whatever  its  height,  the  liquid  will  be  wholly  sus- 
tained by  the  capillary  force. 

It  should  be  noticed  here  that  a  pound  of  water  in  a  tube  of 

What  is  the  principle  of  the  hydrostatic  paradox?  Describe  the  mauuer 
in  which  increase  of  pressure  takes  place. 


126 


NATURAL    PHILOSOPHY. 


Fig.  97. 


one  square  inch  will  fill  the  tube  as  much  higher  than  it  will  the 
box  as  its  surface  is  less,  and  hence  the  law  of  the  equilibrium  is 
the  same  as  in  the  mechanical  powers,  what  is  gained  in  pmcer 
is  lost  in  time  or  space.  A  cubic  foot  of  water,  if  put  into  a  tube 
the  section  of  which  is  one  square  inch,  will  fill  it  to  the  height 
of  1728  inches.  If  such  a  tube  were  inserted  in  a  box  contain- 
ing one  cubic  foot  filled  with  water,  it  would  exert  62^  Ibs.  upon 
every  square  inch  of  its  surface,  or  144  times  62|-  Ibs.  upon  each 
of  the  six  surfaces  of  the  cube. 

It  is  evident  that  a  piston  may  be  fitted  to  the  tube,  and  a 
pressure  exerted  by  mechanical  power  instead  of  a  column  of 
water.  On  this  principle 

The  Hydrostatic  Press  is  con- 
structed. It  consists  of  a  large  and 
a  small  cylinder,  a,  b,  connected  by 
a  tube,  Fig.  97,  with  a  piston,  c,  to 
press  upon  the  water  in  a,  and  a 
larger  piston,  e,  capable  of  sliding  up 
in  the  cylinder  b,  to  which  a  rod  is 
attached  connected  with  a  sliding 
block,  which  is  forced  against  the 
object  to  be  pressed,  d.  £  is  a  fixed 
frame.  The  spaces  below  the  pis- 
tons a  and  e  contain  water.  By  means  of  the  lever,  a  pressure 
of  a  few  pounds  on  the  water  in  a  will  communicate  a  very  great 
force  to  the  piston  e,  the  degree  of  force  depending  upon  the  rel- 
ative number  of  square  inches  in  a  section  of  each  cylinder.  The 
larger  b  is  in  proportion  to  a,  the  greater  will  be  the  power  of  the 
press. 

It  is  obvious  that  there  is  no  limit  to  the  force  which  such  a 
press  may  be  made  to  exert  but  that  which  arises  from  the 
strength  of  the  material  of  which  it  is  constructed. 

This  press  may  be  used  for  pressing  paper,  books,  cotton,  hay, 
and  many  other  substances  where  great  force  is  required.  By 
means  of  a  lever  applied  to  the  cylinder,  the  weight  of  one  man 
is  sufficient  to  tear  up  the  largest  tree  by  its  roots ;  in  fact,  to 
exert  a  pressure  of  more  than  two  millions  of  pounds. 

Compressibility/  of  Water. — By  means  of  this  instrument  the 

Describe  the  hydrostatic  press.     What  limit  is  there  to  its  power? 


RESULTS    OF    PRESSURE. 


127 


compressibility  of  water  may  be  determined,  though  the 
best  instrument  for  this  purpose  is  one  in  which  the 
power  is  exerted  by  means  of  a  screw.  Fig.  98,  upon  a 
column  of  water  contained  in  a  strong  vessel,  a  a,  called 
(Ersted's  Machine.  By  this  instrument,  slightly  mod- 
ified, the  exact  compressibility  of  water  and  some  other 
liquids  has  been  determined.  Water  is  found  to  di- 
minish -220  oo^o-  °f  i*8  volume  for  each  atmosphere,  or 
15  Ibs.  to  the  square  inch.  Alcohol  diminishes 
of  its  volume  for  each  atmosphere  of  pressure. 


PROBLEMS. 

1.  A  submarine  telescope  was  sunk  in  the  East  River,  Ne\v 
York,  to  the  depth  of  30  feet,  when  a  glass  plate,  6  inches  square, 
in  the  side  of  the  box,  near  the  bottom,  was  forced  in.     What 
Was  the  pressure  exerted  upon  the  plate  ? 

Ans.  468f  Ibs. 

2.  A  whale  was  harpooned,  and  drew  the  boat  under  water  to 
such  a  depth  that,  after  having  been  taken  and  the  boat  drawn 
up,  it  was  found  to  be  permanently  compressed  so  as  to  sink  in 
water.     On  the  supposition  that  it  required  a  force  of  540  Ibs.  to 
the  square  inch  to  compress  it,  what  was  the  depth  to  which  it 
was  sunk  ? 

Ans.  1244-16  feet. 

3.  If  a  section  of  the  cylinder  a.  Fig.  97,  is  one  square  inch  in 
surface,  and  that  of  b  4  square  feet,  or  576  square  inches,  what 
pressure  on  b  will  be  exerted  by  100  Ibs.  on  a? 

Ans.  57600  Ibs. 

4.  The  water  in  the  distributing  reservoir  of  the  New  York 
city  water-  works  is  80  feet  above  the  jet  at  the  Park.     What  is 
the  pressure  exerted  upon  a  square  foot  of  pipe  at  the  point  where 
the  jet  issues  ? 

Ans.  5000  Ibs. 

III.  Results  derived  from  the  Laws  of  Pressure.  —  1.  It  re- 
sults directly  from  the  laws  of  pressure  above  considered  that 
1  .  Liquids  will  rise  to  the  same  level  in  tubes  connected  with  a 


128 


NATURAL    PHILOSOPHY. 


Fig.  99. 


common  reservoir,  ivhatever  be  their  size  or  form.  This  is  illus- 
trated in  the  common  tea-pot.  It  may  be  shown  experimentally 
by  means  of  tubes  which  are  curved,  perpendicular,  or  inclined. 

Thus,  if  the  tubes  a  b  c  d  e,  Fig. 
99,  are  connected  with  a  reservoir,  r, 
and  water  poured  into  one  of  them,  it 
will  rise  to  the  same  height  in  all, 
though  their  form  and  capacity  may 
vary  indefinitely. 

It  is  on  this  principle  that  water 
conveyed  in  tubes  will  rise  as  high  as  the  source,  whatever  the 
inequality  of  the  surface  between  the  fountain  and  the  outlet. 
This  fact  appears  not  to  have  been  well  understood  by  the  an- 
cient Romans,  who,  in  the  construction  of  their  aqueducts,  filled 
up  the  valleys  and  cut  through  the  mountains,  in  order  to  form 
a  passage  for  the  water  with  which  their  cities  were  supplied. 

Springs  and  Artesian  Wells  result  from  hydrostatic  pressure. 
— As  the  water  falls  upon  the  surface  of  the  land,  as  b'  b  c  d,  Fig. 
100,  it  sinks  down  among  the  rocks,  which  are  arranged  in  lay- 

Fig.  100. 


a 


ers,  as  b'  b,  c'  c,  d'  d,  and  often  inclined  to  the  horizon  more  01 
less.  Some  of  the  s1  rata,  as  c'  c,  are  porous,  while  others  are 
impervious  to  the  water.  If  the  strata  are  broken,  the  water 
is  forced  out  through  the  crevices,  and  constitutes  a  spring.  If 
the  water-bearing  strata  are  reached  by  means  of  boring,  as  at  a, 
then  the  pressure  will  force  the  water  through  the  aperture. 
These  are  termed  Artesian  Wells.  The  water  which  supplies 
these  wells  may  fall  20,  30,  or  40  miles  from  the  place  where  it 
is  forced  up,  and  hence  the  pressure  will  depend  upon  the  height 
of  the  country  afyove  the  outlet.  Some  of  these  wells  are  1200 
or  1500  feet  in  depth. 


Ou  what  principle  is  it  that  water  may  be  conveyed  over  mountains? 


SPECIFIC    GRAVITY.  129 

Artesian  wells  are  very  common  in  the  salt  regions  of  Western 
Virginia.  By  boring  down  from  800  to  1200  feet  through  the  coal 
strata,  they  reach  a  stratum  which  contains  salt  water,  and,  in 
many  cases,  the  water  flows  out  upon  the  surface,  being  forced 
up,  not  only  by  hydrostatic  pressure,  but  by  the  elastic  force  of 
the  compressed  gases  of  the  coal  beds.  These  gases  are  combus- 
tible, and  are  employed  to  evaporate  the  water  in  order  to  obtain 
the  salt. 

2.  Another  result  derived  from  the  properties  of  a  liquid  and 
the  laws  of  pressure  already  stated  is,  that 

The  surface  of  a  liquid  at  rest  is  always  level  or  horizontal. 
This  fact  is  also  established  by  observation  and  experiment.  Ev- 
ery particle  of  the  surface  is  attracted  toward  the  center  of  the 
earth.  If,  therefore,  we  take  a  large  surface,  as  the  ocean,  it  is 
not  a  plane,  but  spherical ;  the  convexity,  however,  is  very  slight 
for  a  few  feet.  It  deviates  only  8  inches  from  a  plane  for  a  mile, 
2|  feet  for  2  miles,  and  6  feet  for  3  miles.* 

For  all  practical  purposes,  the  surface  of  a  vessel  of  water  is  a 
plane,  and  we  may  therefore  employ  a  liquid  to  determine  wheth- 
er any  surface  is  horizontal.  Hence  the  use  of 

Fig.  101.  The  Spirit  Level. — This  consists 
-=n  of  a  glass  tube,  a,  Fig.  101,  filled 
'  with  alcohol,  excepting  a  small  por- 


tion, which  contains  a  bubble  of  air.  When  the  tube  is  placed 
horizontally,  the  bubble  of  air  will  be  in  its  center  ;  but  if  it  is 
inclined  to  the  horizon  in  any  direction,  the  bubble  will  move  to- 
ward the  elevated  end. 

Instruments  for  engineering,  surveying,  astronomical  observa- 
tions, and  for  leveling  generally  in  the  art  of  building,  are  fur- 
nished with  spirit  levels. 

IV.  Specific  Gravity.  —  When  any  solid  is  immersed  in  a 
liquid,  it  displaces  a  quantity  of  it  just  equal  to  the  bulk  of  the 

*  The  following  formula  will  enable  us  to  estimate  the  variation  for  any 
distance.  Let  L  =  number  of  miles,  and  D  =  depression  in  feet;  then 


What  position  does  the  surface  of  a  liquid  at  rest  assume  ?    Describe  the 
spirit  level.     What  is  its  use  ? 

F  2 


130 


NATURAL    PHILOSOPHY. 


Fig.  102. 


body  immersed.  That  is,  if  the  body  be  one  cubic  foot,  and  im- 
mersed in  water,  it  will  displace  one  cubic  foot  of  that  liquid,  and 
hence  it  must  be  sustained  by  an  upward  pressure  just  equal  to 
the  weight  of  a  cubic  foot  of  water,  or  62^  Ibs.  If  the  solid  is 
heavier  than  water,  it  will  weigh  $2%  Ibs.  less  in  water  than  in 
the  air. 

It  is  on  this  principle,  first  discovered  by  Archimedes,*  that 
the  relative  weights  or  specific  gravities  of  different  substances 
are  determined. 

Specific  gravity  may  be  defined  to  be  the  weight  of  any  body 
compared  with  the  weight  of  an  equal  bulk  or  volume  of  some 
other  body  which  is  taken  as  a  standard. 

Distilled  water  is  taken  as  the  standard  with  which  all  solids 
and  liquids  are  compared,  and  atmospheric  air  is  taken  as  the 
standard  for  gases  and  vapors. 

1.  Specific  Gravity  of  Solids. — In  or- 
der to  determine  the  specific  gravity  of  a 
solid  body,  a  common  balance,  Fig.  102, 
is  employed.  The  body,  suppose  it  to  be 
gold,  is  first  weighed  in  air  and  then  in 
water,,  and  the  loss  of  weight  noted. 
Whatever  it  loses  in  water  will  be  the 
weight  of  a  quantity  of  water  equal  in 
bulk  to  the  gold.  As  many  times,  there- 1 
fore,  as  this  loss  is  contained  in  its  weight 
in  air,  so  many  times  heavier  will  the 
gold  be  than  the  water. 

In  this  case  the  gold  will  lose  in  water  TV"th  of  its  weight  in 

*  Hiero,  the  king  of  Syracuse,  suspecting  that  his  workmen  had  adulter- 
ated a  golden  crown  which  they  had  made  for  him,  employed  Archimedes 
to  detect  the  imposture.  One  day,  while  in  the  bath,  he  noticed  that  his 
body  caused  the  water  to  rise,  and  the  thought  occurred  to  him  that  any 
other  body  of  equal  bulk  would  raise  the  water  to  the  same  height.  He 
immediately  procured  two  pieces,  one  of  gold  and  the  other  of  silver,  equal 
in  weight  to  the  crown,  and  noticed  the  quantity  of  water  each  displaced. 
Then,  on  placing  the  crown  in  the  water,  the  quantity  displaced  was  great- 
er than  that  by  the  gold,  and  less  than  that  by  the  silver ;  and  hence  he  con- 
cluded that  it  was  not  pure  gold,  but  an  alloy  of  these  two  metals. 

Define  specific  gravity.   How  is  the  specific  gravity  of  solids  determined  ? 


SPECIFIC  GRAVITY.  131 

air,  arid  hence  its  specific  gravity  is  19,  or  it  is  nineteen  times 
heavier  than  water. 

If  copper  is  treated  in  the  same  manner,  it  will  lose  £th  of  its 
weight,  and  hence  the  specific  gravity  of  copper  is  9.  To  de- 
termine the  specific  gravities  of  solid  bodies  we  may  apply  the 
following  rule  : 

Divide  the  weight  of  the  body  in  air  by  its  loss  of  weight  in 
water. 

The  reason  of  this  rule  has  already  been  given.  The  loss  of 
weight  is  exactly  the  weight  of  a  mass  of  water  equal  to  the 
mass  of  the  solid  immersed. 

If  the  solid  is  lighter  than  water,  it  must  be  attached  to  a  heav- 
ier body  whose  specific  gravity  is  known,  so  that  it  may  be  whol- 
ly immersed  in  the  water. 

2.  Specific  Gravity  of  Liquids. — The  specific 
gravities  of  liquids  are  determined  in  three  ways  . 
(1.)  By  means  of  a  small  bottle,  Fig.  103, 
which  contains  exactly  1000  grains  of  distilled 
water.  When  the  bottle  is  filled  with  any  other 
liquid,  it  will  contain  more  or  less  than  1000 
grains,  according  as  the  liquid  is  lighter  or  heav- 
ier than  water. 

If  filled  with  sulphuric  acid,  for  example,  it 
will  weigh  1900  grains  ;  if  with  alcohol,  but  800 
grains.     And  hence  the  specific  gravity  of  sul- 
Fig  104.  phuric  acid  is  T9,  and  of  alcohol  0'8. 

(2.)  By  means  of  a  bulb  of  glass,  which  loses  1000 
grains  when  weighed  in  water.  If  this  glass  is  weighed 
in  any  other  liquid,  it  will  lose  more  or  less,  according  to 
the  density  of  the  liquid.  If  it  lose  more  than  1000  grains, 
then  the  liquid  is  lighter  than  water ;  if  it  lose  less  than 
1000  grains,  it  is  heavier  than  water. 

(3.)  By  the  Aerometer.  This  instrument  consists  of  two 
bulbs  of  glass,  A  B,  Fig.  104,  with  a  slender  stem,  a  few 
shot  being  put  in  the  lower  bulb  to  cause  it  to  sink.  The 
stem  is  graduated,  to  determine  the  depth  to  which  it 
sinks  in  different  liquids.  If  it  sink  in  distilled  water  to 

What  is  the  rule  for  ascertaining  the  specific  gravities  of  solids?  H>»w 
are  the  specific  gravities  of  liquids  determined  ?  Describe  the  several 
modes. 


132  NATURAL    PHILOSOPHY. 

zero,  then  in  any  liquid  heavier  than  water  it  will  not  sink  so  far. 
In  any  liquid  lighter  than  water  it  will  sink  below  zero.  The 
numbers  marked  on  the  scale  enable  us  to  ascertain  the  specific 
gravity  of  any  liquid  under  examination. 

This  instrument  is  much  used  in  ascertaining  the  strength  of 
alcoholic  spirits.  The  lighter  they  are,  the  greater  is  the  quan- 
tity of  alcohol  which  they  contain. 

Nicholson's  Gravimeter,  Fig.  105,  is  similar  in  its  construction, 
but  weights  are  applied  to  the  top  of  the  tube.  It  will  evident- 
ly require  different  weights  to  cause  it  to  sink  to  the  same  depth 
in  different  liquids. 

It  may  also  be  used  to  determine  the  specific  gravities  of  sol- 
ids as  well  as  liquids.  The  instrument  is  placed  in  distilled  wa- 
ter, and  weights  added  until  it  sinks  to  a.  The  weights  are 
then  taken  off,  and  the  solid  placed  in  the  cup  c,  with  weights 
sufficient  to  sink  the  instrument  to  a  as  before.  The  weight  of 
the  solid  will  be  equal  to  the  difference  of  the  weights  applied 
in  the  two  cases.  We  have,  therefore,  the  weight  of  the  body 
in  air.  By  placing  the  same  solid  in  the  cup  b,  we  may  ascer- 
tain its  weight  in  water,  for  it  will  be  the  difference  between 
the  weight  which  must  now  be  added  to  sink  the  instrument  to 
a,  and  that  which  was  previously  added  to  the  solid  to  sink  the 
instrument  to  the  same  point;  then,  by  dividing  the  weight  in  air  by  its 
loss  of  weight  in  water,  its  specific  gravity  is  found. 

The  pressure  exerted  by  liquids  will  depend  upon  Fig.iw. 
their  specific  gravities.  Hence,  if  two  liquids  press 
upon  each  other  in  a  curved  tube,  Fig.  106,  their 
heights  will  be  inversely  as  their  specific  gravities. 
That  is,  if  mercury  be  poured  into  one  arm,  a,  and  wa- 
ter into  the  other,  c,  the  water  will  rise  13.5  times  as 
high  as  the  mercury. 

3.  Specific  Gravity  of  Gases. — The  specific  grav- 
ity of  aeriform  bodies  is  determined  by  accurately"?! 
weighing  a  given  quantity  of  air,  and  calling  it  1 . 
Then,  by  weighing  the  same  quantity  of  any  other  gas,  its  spe- 
cific gravity  will  be  directly  ascertained.  Thus,  if  the  air  weigh 
1  grain  and  the  other  gas  2  grains,  its  specific  gravity  is  twice 
that  of  air,  or  2. 

The  following  table  contains  the  specific  gravities  of  several 
substances  : 


1-5 


Describe  Nicholson's  gravimeter.     What  is  the  law  when  liquids  of  dif- 
rent  specific  gravities 
ity  of  gases  determined 


ferent  specific  gravities  press  upon  each  other  ?     How  is  the  specific  grav- 
"  termmed? 


FLOATING    BODIES. 


133 


Sp.  Gr. 

Platinum 21-250 

Gold 19-257 

Silver 10-510 

Mercury 13-568 

Lead 11-352 

Copper 8-895 

Iron 7-780 

Tin 7-200 


Sp.  Gr. 

Zinc 7-00 

Ivory 1-917 

Amber 1-226 

Ebony 1-226 

Cork 0-240 

Alcohol 0-793 

Sulphuric  ether 0-715 

Air>  m  i  me(L  Pressure  ^ 


As  substances  weigh  less  in  water  than  in  air,  it  is  obvious 
that,  if  any  body  is  but  a  little  heavier  than  water,  it  may  be 
moved  about  in  it  with  a  comparatively  slight  force.  It  is  due 
to  this  fact  that  very  large  rocks  are  moved  great  distances  by 
water  and  ice.  The  specific  gravity  of  ice  is  about  TVth  less  than 
that  of  water,  and  where  the  ice  envelops  the  stones  at  the  bot- 
tom of  ponds  and  rivers  during  the  winter,  the  spring  floods,  which 
raise  the  ice,  lift  up  the  rocks  also,  and  float  them  to  a  greater  or 
less  distance. 

The  ice  thus  formed  on  the  shores  of  the  ocean,  especially  in 
high  northern  and  southern  latitudes,  takes  up  large  masses  of 
rock  and  soil,  and  floats  them  toward  the  equator,  until  the  ice- 
berg or  island  entirely  melts  away  by  coming  into  warmer  climes. 

By  ascertaining  the  specific  gravity  of  an  irregular  body,  we 
may  determine  its  size  or  solid  contents ;  for,  by  noting  the  quan- 
tity of  water  which  it  will  displace,  and  allowing  a  cubic  foot  for 
every  62£  Ibs.,  the  size  is  readily  obtained. 

V.  Floating  Bodies. — Bodies  lighter  than  liquids  float  on  their 
surfaces,  and  the  parts  immersed  will  displace  a  quantity  of  the 
liquid  equal  in  weight  to  the  iveight  of  the  floating  body.  This 
fact  is  a  direct  result  of  the  upward  pressure  of  liquids ;  for,  in 
order  to  sustain  the  body,  there  must  be  an  upward  pressure  just 
Fig.  107.  equal  to  its  weight. 

It  is  also  proved  by  experiment.     Thus  : 

Exp. — Fill  a  vessel,  A,  Fig.  107,  with  water,  and 
place  in  it  a  ball  of  wood.  The  water  which  will 
flow  out  at  a,  when  weighed,  will  exactly  equal  the 
weight  of  the  wood. 

Bodies  thus  floating  on  the  surface  of  liquids 

By  what  means  are  rocks  transported  ?  How  can  the  size  of  an  irregu- 
lar solid  be  determined  ?  What  quantity  of  a  liquid  does  a  floating  body 
displace  f 


134  NATURAL    PHILOSOPHY. 

must  have  their  centers  of  gravity  supported  ;  and  hence,  in  ordei 
that  they  may  be  supported,  these  centers  must  be  in  a  line  with 
the  center  of  gravity  of  the  displaced  liquid  ;  so  that  a  body  on 
the  water  will  have  its  center  of  gravity  either  directly  above  or 
below  that  of  the  displaced  liquid  ;  but  if  this  center  be  situated 
above  a  certain  point,  which  must  be  determined  for  each  sub- 
stance, called  the  metacenter,  the  body  will  be  upset. 

"  A  great  inventor  (in  his  own  estimation)  published  to  the 
world  that  he  had  solved  the  problem  of  walking  safely  upon  the 
water,  and  he  invited  a  crowd  to  witness  his  first  essay.  He 
stepped  boldly  upon  the  waves,  equipped  in  bulky  cork  boots, 
which  he  had  previously  tried  in  a  butt  of  water  at  home  ;  but 
it  soon  appeared  that  he  had  not  pondered  sufficiently  on  the  cen- 
ter of  gravity  and  of  flotation,  for,  on  the  next  instant,  all  that 
was  to  be  seen  of  him  was  a  pair  of  legs  sticking  out  of  the  wa- 
ter, the  movements  of  which  showed  that  he  was  by  no  means 
at  his  ease.  He  was  picked  up  by  help  at  hand,  and,  with  his 
genius  cooled,  and  schooled  by  the  event,  was  conducted  home." 
— Arnott. 

The  human  body,  when  the  lungs  are  filled  with  air,  is  light- 
er than  water,  and  will  float  upon  it ;  but  if  one  attempt  to  walk 
on  the  water,  the  center  of  gravity  will  sink  so  low  as  to  im- 
merse all  but  the  top  of  his  head.  If  one  could  lay  upon  his 
back  with  only  his  face  out  of  water,  he  would  float  upon  its 
surface  in  safety. 

The  art  of  swimming  depends  upon  the  power  of  striking  the 
water  with  the  limbs,  which,  by  its  reaction,  supplies  the  addi- 
tional force  requisite  to  keep  the  head  above  the  water.  When 
persons  fall  into  the  sea  from  the  mast  of  a  vessel,  they  often  sink 
so  far  that  the  pressure  compresses  the  air  in  their  lungs,  and 
they  never  rise  to  the  surface. 

When  ships  float  upon  water  they  observe  the  law  above  con- 
sidered ;  but  as  they  roll  in  different  directions,  and  as  their  load- 
ing is  thereby  liable  to  alter  its  position,  their  center  of  gravity 

What  position  will  any  body  assume  when  thrown  on  water  ?  In  what 
way  may  persons  float  upon  water?  Why  do  persons  never  rise  when 
they  fall  into  the  sea  from  the  mast  of  a  vessel  ? 


FLOATING    BODIES.  135 

may  be  thrown  above  the  metacenter.  Hence  the  importance 
of  so  stowing  their  cargo  as  to  sink  the  center  of  gravity,  as  low 
as  possible  ;  for  the  lower  it  is,  the  less  is  its  disturbance,  and,  of 
course,  the  less  is  the  danger  to  the  vessel  of  being  capsized. 

A  ship  in  a  close  dock  or  a  canal  boat  in  a  lock  are  supported 
by  displacing  a  quantity  of  water  equal  to  their  immersed  por- 
tions, though  a  very  small  quantity  of  water,  on  the  principle  of 
the  hydrostatic  paradox,  may  be  made  to  float  the  largest  ships. 

A  boat  in  the  lock  of  a  canal  is  sustained  by  a  small  quantity 
of  water  on  the  same  principle,  and  it  is  only  necessary  to  ascer- 
tain, in  such  cases,  the  height  of  the  column  of  water  and  the  di- 
mensions of  the  vessel,  to  determine  its  weight.  In  this  way 
canal  boats  are  sometimes  weighed.  Sea  water  is  rather  more 
dense  than  fresh  water,  and  hence  a  ship  draws  rather  less  wa- 
ter in  the  ocean  (about  Jj th  less)  than  in  a  river  or  lake. 

Liquids  of  different  specific  gravities  float  upon  each  other,  as 
oil  and  ether  upon  water,  water  upon  mercury,  cream  upon  milk. 

Fish  are  of  the  same  specific  gravity  as  water,  and  they  are 
enabled  to  rise  and  fall  by  means  of  an  air  bladder  within  them, 
which  may  be  contracted  or  enlarged  at  pleasure  ;  so  that  a  fish 
in  his  native  element  is  said  to  be  destitute  of  weight.  The 
question  was  once  proposed  why  a  pail  of  water  would  weigh 
the  same  with  a  fish  in  it  that  it  would  when  the  fish  was  taken 
out,  and  several  learned  explanations  were  given  ;  but  when 
the  question  was  proposed  to  Franklin  by  some  of  the  French 
savans,  he  suggested  that  they  should  try  the  experiment,  and 
ascertain,  in  the  first  place,  whether  it  were  a  fact. 

Life  Preservers  and  Life  Boats. — It  is  evident  that  bodies 
heavier  than  water  may  be  made  to  float  upon  its  surface  by  at- 
taching to  them  bodies  lighter  than  water.  On  this  principle 
life  preservers  and  life  boats  are  constructed.  A  bag  of  air  placed 
around  the  body  just  under  the  arms  will  cause  it  to  float,  and 
to  sustain  a  pressure  proportioned  to  its  size. 

How  should  the  cargo  in  a  vessel  be  stowed  ?  Does  a  ship  in  a  close 
dock  displace  a  quantity  of  water  equal  to  its  immersed  portions?  How 
does  the  specific  gravities  of  fresh  and  salt  water  compare  with  each  other  ? 
On  what  principle  are  life  preservers  and  life  boats  constructed  ? 


136  NATURAL    PHILOSOPHY. 

Sunken  vessels  are  sometimes  raised  by  means  of  air-bags 
placed  under  them  and  filled  with  air. 

Life  boats  are  made  partly  of  cork,  and  some  have  also  air- 
bags  fitted  to  their  sides,  so  that  they  will  not  sink,  though  filled 
with  water. 

People  in  China,  who  live  in  boats  upon  the  rivers,  attach  hol- 
low balls  of  some  light  substance  to  the  heads  of  their  children,  to 
prevent  them  from  sinking  when  they  chance  to  fall  into  the  water. 

PROBLEMS. 

1.  It  is  required  to  determine  the  quantity  of  gold  and  copper 
in  a  chain  composed  of  an  alloy  of  these  metals,  which  weighs  2 
ounces  in  the  air,  and  1  ounce  17  pennyweights  in  water  ? 

Ans.  Gold,  171  pennyweights;  copper,  22|  pennyweights. 

2.  If  a  cannon  ball,  whose  specific  gravity  is  seven  times  that 
of  water,  were  dropped  into  the  ocean,  at  what  depth  would  it 
float  ?* 

*  This  problem  requires  considerable  knowledge  of  algebra.  Those 
not  acquainted  with  algebra  may  omit  it.  The  following  is  one  mode  of 
solving  it.  It  proceeds  on  the  supposition  that  one  column  of  34  feet  at 
the  surface  pi'oduces  a  compression  of  TTO^OT  °f  itself.  Suppose  the  whole 
depth  to  be  divided  into  columns  of  34  feet  each.  Let  the  amount  of  com- 
pression TT2iTo7  be  represented  by  R,  and  the  height  of  one  column  by  =  h. 
Let  d  represent  the  density  of  the  first  column. 

d,,         "  "  at  the  depth  of  n  such  columns. 

As  the  density  of  each  column  increases  an  R  part  of  the  preceding  col- 
umn, 

We  shall  have  the  density  of  the  first  column  =d, 

"  "  second  " 

"  "  "  third      "       =d(l-f-R)2, 

"  "  "  fourth    "       =d(l-j-R)3, 

"  "  "  nth         "       =d(l-fR)n, 

But  as  the  first  column  is  not  compressed,  the  density  of  the  column  at  the 
point  where  the  ball  will  float,  or 


and  at  this  point  the  water  is  seven  times  the  density  of  the  surface,  or  7d  y 
hence 


Log.  (1+R)' 
and  the  depth  from  the  surface  would  be 

Log.  7      \        34    /       -8450980  ..  . 

^  miles  nearly- 


HYDRAULICS.  137 

3.  A  loaded  ship  was  found  to  draw  20  feet  of  water  ;  on  the 
supposition  that  the  part  immersed  was  equal  to  a  block  100 
feet  long,  10  high,  and  20  wide,  what  is  the  weight  of  the  ship  ? 

Ans.  625  tons. 

4.  An  iceberg,  of  a  conical  shape,  was  found  to  rise  250  feet 
above  the  water.     The  part  which  appeared  was  estimated  to 
contain  5000  cubic  feet.     What  was  the  size  of  the  berg  ? 

Ans.  50,000  cubic  feet. 

To  what  depth  did  it  sink  below  the  water,  on  the  supposition 
that  its  center  of  gravity  and  center  of  magnitude  coincided  ? 

Ans.  2250  feet. 

5.  Two  gold  chains  were  placed  in  a  vessel  full  of  water,  and  the 
weight  of  water  which  overflowed  was  found  to  be  6  ounces.  What 
were  the  solid  contents  of  the  chains  ?     Ans.   104     cubic  inches. 


SECTION  II.—  HYDRAULICS. 

The  motion  of  liquids  is  generally  due  to  gravity,  though  it 
often  results  from  other  forces;  but,  oiuing  to  the  peculiar  proper- 
ties of  liquids,  the  laws  of  motion,  derived  from  theory,  are  some- 
what modified  in  practice. 

I.  The  velocity  of  a  liquid  spouting  from  an  orifice  in  the 
Bide  of  a  vessel  is  just  equal  to  that  which  a  falling  body  would 
acquire  in  descending  through  the  perpendicular  height  of  the 
column  above  the  orifice. 

II.  The  quantity  of  liquid  discharged  from  any  vessel  is  mod- 
ified by  friction  and  the  crossing  of  currents  at  the  orifice. 

III.  The  quantity  is  also  modified  by  conducting  tubes,  which, 
if  short,  increase,  and  if  long,  diminish  the  quantity  of  efflux. 

IV.  A  jet  ofivater  issuing  from  the  side  of  a  vessel  describes 
the  curve  of  a  parabola  ;  and  the  random  from  a  jet  at  the  cen- 
ter of  the  column  is  greatest,  ivhile  those  at  equal  distances  from 
the  center  above  and  below  have  the  same  random. 

V.  When  liquids  flow  in  rivers,  pipes,  and  canals,  the  velocity 
of  the  stream,  at  any  part  of  its  course,  is  inversely  as  the  area 
of  the  section  of  that  part. 

VI.  Liquids  resist  the  motion  of  bodies  passing  through  them 
in  the  ratio  of  the  square  of  the  velocity. 


138  NATURAL    PHILOSOPHY. 

VII.  Liquids  are  practically  applied  to  move  machinery  by 
means  ofivheels  which  are  placed  either  vertically  or  horizontal- 
ly, and  are  moved  by  the  force  of  the  stream. 

HYDRAULICS*  treats  of  the  motion  of  liquids,  and  of  the  ma- 
chines which  are  put  in  motion  by  them. 

The  motion  of  liquids,  whether  they  flow  in  pipes,  rivers,  01 
canals,  results  from  the  attraction  of  gravitation ;  but,  owing  to 
the  peculiar  properties  of  a  liquid,  and  the  action  of  this  force  al- 
ready noticed,  page  1 20,  their  motions  are  subject  to  special  laws, 
different  somewhat  from  those  of  solids,  so  that  the  laws  of 
their  motion  derived  from  theory  must  be  modified  in  actual  ex- 
perience, in  order  to  be  fully  relied  upon.  That  is,  when  we  de- 
termine how  a  liquid  should  move  by  the  laws  of  motion,  we  find, 
by  experiment,  a  considerable  deviation  from  the  theoretical  law. 
We  must  therefore  combine  experiment  with  theory  in  order  to 
arrive  at  the  exact  truth. 

I.  Laivs  of  the  Efflux  of  Liquids  flouring  from  the  Bottom  or 
Sides  of  Vessels. — As  the  motion  of  any  liquid  is  due  to  the  force 
of  gravitation,  if  we  make  an  aperture  in  the  bottom  or  the  side 
of  a  cylindrical  or  prismatic  vessel  filled  with  water, 

1.  The  velocity  ivith  ivhich  it  will  flow  out  will  be  equal  to 
that  which  a  falling,  body  ivould  acquire  in  falling  from  the 
surface  of  the  liquid  to  the  opening  whence  the  liquid  escapes. 

The  truth  of  this  proposition,  which  is  called  the 

Torricellian  Theorem,  will  be  evident  when  we      Fif  108 
consider  that  the  stratum,  Fig.  108,  next  to  the  ori- 
fice, is  forced  out  not  only  by  its  own  gravity,  but  by 
the  pressure  of  every  other  stratum  above  it  to  the 
surface  ;  so  that  the  top  stratum,  instead  of  falling 
freely  to  the  orifice,  imparts  its  own  motion  to  the  $£&& 
second,  and  then  to  the  third,  and  so  on  until  it  reach-       ™ 
es  the  stratum  at  the  orifice,  which  receives  this  motion,  and 

*  iidup,  water,  and  aJMof,  a  torrent. 

What  is  the  meaning  of  hydraulics?      What  gives  rise  to  the  motion  of 
Mqu»-l3?     Of  what  value  is  the  theory  of  the  motion  of  liquids?     What  is 
H  "»w  of  the  efflux  of  a  liqtaid  ? 


LAWS    OF    SPOUTING    LIQUIDS.  139 

flows  out  with  the  same  velocity  which  the  first  would  have  ac- 
quired if  free  to  fall  through  the  same  distance.  If,  therefore,  we 
know  the  height  of  the  column,  we  may  apply  to  it  the  laws  of 
falling  bodies  to  determine  the  velocity  of  efflux  ;  for  it  is  evident 
that  the  velocity  will  depend  upon  the  height  of  the  column  or 
depth  of  the  orifice  below  the  surface  of  the  liquid,  and  not  upon 
the  quantity  of  liquid  or  size  of  the  vessel. 

Now  the  velocities  of  a  falling  body  are  as  the  square  roots  of 
the  spaces  through  which  it  falls,  page  62,  and  hence  the  veloci- 
ties of  jets  of  water  issuing  from  the  side  or  bottom  of  a  vessel 
are  also  as  the  square  roots  of  the  depth  of  the  orifices  below  the 
surface.  That  is,  the  velocity  at  16  inches  below  the  surface  is 
twice  as  great  as  at  4  inches,  the  square  roots  of  1 6  and  4  being 
4  and  2.  By  observing  this  law  we  may  determine 

2.  The  quantity  discharged  from  the  same  orifice  at  different 
depths.     For  as  the  quantity  discharged  will  be  as  the  velocity, 
an  aperture  at  16  inches  below  the  surface  will  discharge  twice 
the  quantity  in  the  same  time  as  one  at  4  inches  ;  at  64  inches, 
four  times  the  quantity  will  be  discharged.     This  principle  is  of 
great  practical  importance  in  determining  the  quantity  of  water 
which  will  issue  from  a  given  orifice  at  the  bottom  of  dams  and 
reservoirs  where  the  depth  is  known. 

3.  If  we  apply  the  law  of  falling  bodies  to  a  liquid  issuing 
from  an  orifice  of  one  square  foot  of  surface,  the  velocity  at  the 
depth  of  16*  feet  will  be  32  feet  per  second,  and  therefore  the 
quantity  of  liquid  discharged  will  be  32  cubic  feet  per  second. 
The  same  orifice  at  the  depth  of  4  feet  will  discharge  but  half  as 
much  in  the  same  time.     This  law,  however,  is  deviated  from 
in  actual  practice,  as  we  shall  presently  show  ;  yet,  if  we"  assume 
it  to  be  strictly  true,  it  may  be  applied  to  the  solution  of  the  fol- 
1  owing 

*  The  fraction  y^h  is  omitted  for  the  sake  of  rendering  the  expression 
more  simple. 

How  is  the  velocity  of  a  liquid  issuing  from  the  side  of  a  vessel  determ- 
ined ?  What  law  controls  the  quantity  discharged  at  different  depths  be- 
low the  surface  ? 


140 


NATURAL    PHILOSOPHY. 


PROBLEMS. 

1.  There  is  a  certain  dam,  16  feet  in  height,  kept  constantly 
full  of  water.     It  is  required  to  determine  the  quantity  of  water 
discharged  per  hour  by  a  tube  at  the  bottom,  a  section  of  which 
contains  4  square  feet  of  surface  ?         Ans.  460,800  cubic  feet. 

2.  Three  men,  A,  B,  and  C,  own  a  dam  which  is  16  feet  high, 
out  of  which  each  wishes  to  draw  water.     A  inserts  a  tube,  the 
section  of  which  is  one  square  foot  in  surface  at  the  bottom  ;  B 
inserts  a  tube  of  2  square  feet,  9  feet  from  the  top  ;  and  C  inserts 
a  tube  of  3  square  feet,  4  feet  from  the  top.     It  is  required  to 
determine  the  quantity  of  water  which  each  would  draw  from 
the  dam  in  the  space  of  24  hours. 

Ans.  A=2,764,800;  B=4,147,200;  0=4,147,200  cub.  feet. 

3  •  In  the  side  of  a  dam  an  aperture  of  4  square  feet  was  made, 
which  was  found  to  discharge  1.00  cubic  feet  of  water  per  second. 
At  what  depth  below  the  surface  of  the  water  was  the  aperture 
made  ?  Ans.  9|f  feet. 

4.  A  certain  pipe  at  the  depth  of  16  feet  was  found  to  dis- 
charge 384  cubic  feet  of  water  per  second.  What  was  the  size 
of  the  pipe  ?  Ans.  12  square  feet. 


4.  If  a  tube  bent  upward  be  inserted  in  the  ori- 
fice, the  jet  ought  to  rise  to  a  height  equal  to  that 
of  the  surface  of  the  liquid  in  the  vessel ;  for  a  body 
projected  upward,  page  65,  with  the  velocity  ac- 
quired in  falling  through  a  given  space,  will  rise  to 
the  same  height  as  that  space ;  but  in  the  case  of 
liquids  the  law  is  deviated  from  more  or  less. 

For  we  find  by  experiment  that  the  jet,  Fig.  109, 
falls  far  below  the  surface  of  the  liquid.  This  is 
due  to  the  greater  resistance  of  the  air.  The  jet  is 
somewhat  divided  in  its  ascent,  and  presents  a  larg- 
er surface  to  the  air.  The  law  is  strictly  true  only 
when  a  solid  or  liquid  body  moves  in  a  space  void  B 
of  air 


109. 


To  what  height  will  a  liquid  spout  from  a  bent  tube  inserted  in  the  sidt 
of  a  vessel  filled  with  water  1 


LAWS    OF    SPOUTING    LiaUIDS.  141 

For  the  same  reason,  water  falling  through  the  air  upon  a 
wheel,  from  a  given  height,  will  be  retarded  in  its  descent,  and 
the  force  of  its  fall  will  be  less  than  when  it  is  conducted  through 
a  tube,  though  in  theory  the  effects  ought  to  be  exactly  equal. 

In  all  the  above  cases  the  vessel  is  supposed  to  be  kept  con- 
stantly full  of  liquid,  and,  of  consequence,  the  velocity  of  the  jet 
always  uniform,. 

5.  But  if  a  vessel  be  emptied  from  an  orifice  in  the  side,  then 
the  velocity  of  the  jet  and  of  the  descending  surface  will  be  uni- 
formly retarded ;  for  as  the  pressure  will  constantly  diminish, 
the  velocity  of  the  jet,  and,  consequently,  the  quantity  of  liquid 
discharged,  must  also  diminish,  and  the  surface,  as  it  descends, 
must  be  in  the  same  condition  as  that  of  a  body  projected  direct- 
ly upward,  and  subjected  to  the  retarding  influence  of  gravity ; 
that  is,  the  velocity  of  the  surface  must  constantly  diminish;  and 
as  the  spaces  through  which  a  body  will  fall  in  several  success- 
ive seconds  of  time  are  as  the  odd  numbers  1,  3,  5,  7,  9,  the 
spaces  described  by  the  descending  surface  in  equal  successive 
portions  of  time  will  be  as  these  numbers  inverted,  or  9,  7,  5,  3,  1. 
If,  therefore,  a  vessel  be  divided  into  portions  having  the  same 
ratio  as  these  numbers,  and  then  filled  with  water,  it  may  be  made 
to  measure  time.  Such  a  tube,  in  principle,  constitutes  the  Clep- 
sydra, or  water-clock,  which  was  formerly  used  as  a  time-piece. 

From  these  two  laws  it  follows  that  the  quantity  of  liquid  dis- 
charged in  a  given  time  from  a  vessel  kept  constantly  full,  is 
double  that  discharged  if  the  vessel,  after  being  filled,  is  simply 
allowed  to  empty  itself  to  the  level  of  the  same  orifice  ;  just  as  a 
body  projected  downward  with  uniform  velocity  will  describe 
double  the  space  it  would  if  projected  upward  with  the  same  ve- 
locity, under  the  retarding  influence  of  gravity. 

Prod.  1.  A  certain  dam,  16  feet  deep,  was  drained  by  an  ori- 
fice of  4  square  feet  in  the  bottom  in  24  hours.  Required  the 
quantity  of  water  which  it  contained. 

Ans.  5,529,600  cubic  feet. 

What  resistance  does  a  jet  meet  with  in  rising  or  falling  ?  When  a  ves- 
sel empties  itself  from  an  orifice,  according  to  what  law  does  the  surface 
descend  ?  What  is  the  Clepsydra  ? 


142 


NATURAL    PHILOSOPHY. 


2.  There  is  a  pipe  64  feet  high,  and  1  foot  in  diameter,  filled 
with  water.  How  long  will  it  take  to  empty  it  from  an  orifice 
in  the  bottom  of  1  square  inch  in  surface  ? 

Ans.  3m.  4Gs.+  . 

II.  Influence  of  the  Orifice  upon  the  Quantity  of  Liquid 
disclutrged. 

I .  When  an  aperture  is  made  in  the  side  of  a  vessel,  and  the 
actual  velocity  and  quantity  discharged  in  a  given  time  are  accu- 
rately noted,  it  is  found  that  the  velocity  and  the  quantity  are 
each  less  than  what  is  demanded  by  the  laws  above  considered. 

This  is  due  to  the  crossing  of  currents  near  the  orifice,  and 
also  to  the  fact  that  those  portions  immediately  above  the  open- 
ing have  a  greater  velocity  at  first  than  those  on  the  opposite 
sides;  the  consequence  of  this  is,  that  the  center  of  the  jet,  which 
flows  with  a  velocity  in  proportion  to  the  pressure,  will  be  "  sur- 
rounded by  lines  of  water  whose  velocity  diminishes  in  propor- 
tion as  they  approach  the  edge  of  the  aperture,"  and  this  causes 
a  contraction  of  the  stream  as  it  issues  from  the  ori- 
fice, as  s  s',  Fig.  110,  called  "the  contracted  vein," 
so  that  the  area  of  a  section  of  the  jet,  s  s',  just  after 
it  reaches  the  orifice,  is  only  two  thirds  that  of  the 
aperture,  and,  consequently,  only  two  thirds  of  the 
quantity  is  discharged  which  theory  requires. 

The  greater  velocity  of  the  water  through  the 
center  of  the  orifice,  and  the  influence  of  the  cur- 
rents flowing  from  the  sides  toward  the  center  of 
the  jet,  may  be  illustrated  by  making  an  orifice  in 
the  center  of  the  bottom  of  any  vessel,  Fig.  Ill, 
and  putting  into  the  water  powdered  amber.  It 
will  be  found  that  the  particles  of  amber  will  de- 
scend in  right  lines  until  they  arrive  within  three  or 
four  inches  of  the  aperture,  and  then  they  will  flow 
toward  it.  This  meeting  of  the  currents  at  the  cen- 
ter retards  the  motion  of  the  water  near  the  sides  of 
the  vessel,  and  produces  a  whirl  in  the  form  of  a  conical  cavity, 
a,  upon  the  surface.  This  cavity  increases  in  depth,  so  that  an 
aperture  is  made  quite  through  the  center  of  the  jet  before  all  the 

What  influence  has  the  orifice  upon  the  quantity  of  liquid  discharged  ? 
and  to  what  is  this  influence  due  ?  What  is  the  cause  of  the  funnel-shaped 
cavity  when  liquids  flow  through  a  hole  in  the  bottom  of  any  vessel  ? 


Fig.  110. 


INFLUENCE    OF    CONDUCTING    TUBES.  143 

water  is  discharged  ;  or,  as  the  central  portions  have  a  greater 
velocity,  the  pressure  of  the  atmosphere  aids  in  opening  a  pas- 
sage directly  through  the  jet. 

According  to  the  experiments  of  Bossut,  the  actual  discharge 
per  minute  compared  with  the  computed  discharge  is  as  follows  : 

Height  of  Liquid.  Computed.  Actual. 

1  foot  above  the  orifice,  4,427  cubic  inches.  2,812  inches. 

5  feet  "  "  10,123  "  "  6,277  " 

10  "  "  "  14,317  "  "  8,860  " 

15  "  "  "  17,533  "  "  10,821  " 

It  will  be  perceived  that  only  about  64  per  cent.,  or  two  thirds 
the  quantity  is  discharged  which  the  theory  requires ;  and  on 
this  account,  therefore,  an  allowance  must  always  be  made  when- 
ever it  is  required  practically  to  determine  the  quantity  discharg- 
ed from  any  dam  or  reservoir.  The  answers  to  the  problems  on 
page  140  must  be  reduced  one  third  in  order  to  correspond  to  the 
quantity  actually  discharged. 

III.  Influence  of  Conducting  Tubes  upon  the  Quantity  of 
Liquid  discharged. — When  tubes  are  inserted  in  the  orifice  of 
a  vessel,  a  still  further  modification  of  the  quantity  of  efflux  takes 
place. 

1 .  If  a  short  tube  be  inserted  in  the  orifice,  having  the  exact 
form  and  length  of  the  jet  from  the  orifice  to  the  point  where  it 
contracts  when  the  orifice  is  a  thin  wall,  no  effect  will  be  pro- 
duced upon  the  quantity  discharged  ;  but  if  the  pipe  is  cylindrical, 
and  not  more  than  four  times  the  length  of  its  diameter,  the 
quantity  discharged  will  be  much  greater,  in  a  given  time,  than 
when  the  efflux  is  made  through  the  same  aperture  in  the  side 
of  the  vessel.  This  increase  is  sufficient  to  raise  the  quantity 
discharged  from  64  to  84  per  cent,  of  the  amount  which  theory 
requires. 

The  increased  quantity  discharged  by  the  tube  is  due  in  part 
to  the  adhesion  of  the  liquid  to  the  sides  of  the  tube,  which  pre- 
vents the  contraction,  and  in  part  to  the  pressure  of  the  air,  which 
accelerates  the  flow  of  the  liquid  into  the  tube,  but  retards  its 
efflux  from  it.  The  result  of  this  is,  that  the  tube  is  kept  con- 
stantly full. 

What  is  the  effect  of  conducting  tubes  on  the  quantity  of  liquid  dis- 
charged ?  How  is  the  effect  explained? 


144 


NATURAL   PHILOSOPHY. 


That  the  pressure  of  the  air  has  this  effect  is  proved  by  the 
fact  that  the  quantity  of  efflux  is  not  increased  by  conducting 
tubes  if  the  liquid  flow  into  a  vacuum.  The  velocity  of  the  efflux 
is  diminished  by  the  tube,  but,  owing  to  the  twTo  causes  above 
stated,  the  quantity  discharged  in  a  given  time  is  greater  than  it 
would  be  through  a  thin  wall,  because  the  tube  is  kept  constant- 
ly full. 

2.  Lateral  Pressure  of  Liquids  in  Conducting  Tubes. — If 
long  tubes  are  inserted  jri  the  sides  of  a  vessel,  the  quantity  of 
liquid  discharged  will  be  diminished,  because  of  the  lateral 
pressure,  and  consequent  friction  against  the  sides  of  the  tube. 
The  smaller  the  tube  is  in  proportion  to  its  length,  the  greater 
will  the  resistance  become.     If  a  tube  project  within  the  vessel, 
it  will  also  diminish  the  quantity  of  efflux. 

3.  Now  the  lateral  pressure  is  equal  on  the  whole  interior  sur- 
face of  a  tube  ;  if,  therefore,  the  end  of  the  tube  be  stopped,  and 
an  aperture  made  in  the  side,  this  pressure  will  be  removed  from 
that  side  while  it  remains  upon  the  opposite  side.     This  pressure 
will  tend  to  force  the  tube  in  a  direction  opposite  to  that  from 
which  the  liquid  flows.     This  is  called 

The  reaction  produced  by  efflux.  It  is  on 
this  principle  that  Barker's  Mill  or  Seigner's 
Water  Wlieel  is  constructed.  It  consists  of  a 
hollow  cylinder,  c,  Fig.  112,  revolving  on  an 
axis,  with  horizontal  tubes  inserted  near  the 
lower  end,  b  e,  and  perforated  by  apertures  in 
the  sides,  a  d,  near  the  ends.  When  the  cyl- 
inder is  filled  with  water  from  a  pipe,  p,  and 
the  pressure  is  removed  on  opposite  sides  of 
the  arms  a  and  d,  the  reaction  produced  by 
pressure  upon  the  sides  b  and  e  turns  the 
wheel  with  great  velocity  in  the  direction 
indicated  by  the  arrows.  As  the  pressure  de- 
pends upon  the  height,  a  small  quantity  of  water  may  be  made 
to  exert  very  great  force. 

4.  When  water  is  flowing  in  a  pipe,  if  it  is  suddenly  stopped 
a  very  considerable  force  is  exerted  by  its  reaction,  sufficient,  in 

What  effect  has  the  lateral  pressure  of  liquids  in  long  tubes?     Describe 
Barker's  mill. 


Fig.  112. 


RANDOM    OF    SPOUTING    LIQUIDS, 


145 


Fig.  113. 


some  cases,  to  burst  the  tube.  This  is  due  to  its  inertia.  The 
stream,  as  it  is  confined  in  a  tube,  acts  like  a  solid  bar.  A  high- 
ly practical  use  is  made  of  this  force,  in.  connection  with  the  elas- 
ticity of  the  air,  to  raise  water  to  various  elevations, -and  to  pro- 
duce a  constant  flow.  This  is  effected  by  an  instrument  called 
The  Hydraulic  Ram. — Thus,  a  tube,  p, 
Fig.  113,  is  made  to  conduct  water  from  a 
spring,  which  must  be  elevated  a  few  feet,  so 
as  to  give  considerable  velocity  to  the  stream. 
At  the  end  of  the  tube  there  is  an  upright 
pipe,  c,  in  which  a  valve,  a,  plays,  and  per- 
mits a  portion  of  the  water  to  pass  by  it  un- 
til it  is  raised  to  the  top,  when  it  suddenly 
stops  the  flow.  In  the  side  of  the  tube  there 
is  a  valve,  i,  opening  into  a  strong  air-cham- 
ber, 6.  When  the  stream  is  stopped  at  c, 
its  reaction  opens  the  valve  at  i,  and  forces  into  b  a  portion  of 
water.  This  relieves  the  pressure  upon  the  valve  a,  and  it  falls 
to  the  bottom  of  the  tube,  and  is  again  raised  up  by  the  force  of 
the  stream,  c?  is  a  tube  to  conduct  the  water  to  any  required 
height.  As  the  air  becomes  compressed  in  b,  it  presses  upon  the 
surface  of  the  water,  and  renders  the  stream  from  d  constant. 

IV.  Form  of  the  Jet  flowing  from  the  Sides  of  a  Vessel,  and 
its  Random,  or  Horizontal  Distance  from  the  Base  of  the  Vessel. 
Fig.  114.  1.  A  jet  of  water,  or  of  any  other  liquid, 

which  flows  from  the  sides  of  a  vessel,  de- 
scribes in  its  descent  the  curve  of  a  parab- 
ola. Thus,  let  a  cylindrical  vessel,  Fig 
114,  be  filled  with  water,  and  a  b  c  three 
orifices  in  its  side  :  c  at  the  center,  and  a 
and  b  at  equal  distances  from  c.  The  three 
jets  will  describe  a  parabola  ;  for  it  is  evi- 
dent, setting  aside  the  resistance  of  the  at- 

mosphere,  that  the  water  will  be  in  the 

^1\  «  condition  of  a  projectile  which  moves  un- 
der two  forces,  the  force  of  projection  and  that  of  gravity  (see 
page  72).  If  now  a  semicircle  be  described  upon  the  side,  and 
lines  drawn  from  a,  5,  and  c  perpendicular  to  the  side  and  meeting 
the  circle,  it  is  found  that 

What  is  the  principle  of  the  hydraulic  ram  1  What  is  its  use  1  Describe 
the  hydraulic  ram.  What  is  the  form  of  the  jet  flowing  from  the  sides  of 
a  vessel  ? 


146  NATURAL    PHILOSOPHY. 

2.  The  random  of  each  jet,  a,  b,  c>  ivill  be  just  double  the  length 
of  these  lines,  which  are  called  the  ordinates  to  the  curve.  This 
law  results  directly  from  the  laws  of  falling  bodies,  the  force  of 
projection  being  the  pressure  of  the  liquid,  The  jets  from  a  and 
b  will  reach  the  point  d,  which  is  twice  the  distance  a  e,  b  i. 
The  jet  c  will  reach  a  point  which  is  equal  to  twice  cf.  Hence 
the  jet  which  spouts  4rom  the  center  of  the  vessel  will  have  tho 
greatest  random,  and  the  two  jets  equally  distant  from  c  will  havo 
the  same  random,  or  spout  to  exactly  the  same  distance  from  the 
base  of  the  column. 

It  should  be  observed,  however,  that  when  liquids  spout  against 
the  air,  they  meet  with  a  resistance  which  gives  the  jet  the  same 
form  that  is  given  to  projectiles,  and  they  actually  describe  the 
Balistic  curve  instead  of  the  curve  of  a  parabola.  It  is  only  in  a 
vacuum  that  the  curve  of  a  parabola  is  actually  described  either 
by  a  solid  or  a  liquid  (see  page  72).  The  degree  of  resistance 
will  of  course  depend  upon  the  velocity  of  the  jet.  If  the  ve- 
locity is  doubled,  the  resistance  will  be  four  times  as  great. 

V.  Motion  of  Liquids  in  Pipes,  Rivers,  and  Canals. — The 
motion  of  liquids  in  rivers  and  canals  is  modified  by  their  depth 
and  width,  or  by  the  size  of  the  channel.  If  the  channel  or  pipe 
is  constantly  full,  the  velocity  will  be  greatest  where  the  channel  is 
smallest,  and  least  where  the  channel  is  largest ;  in  other  words, 

The  velocity  of  the  stream  in  any  part  of  its  course  is  inverse- 
ly as  the  area  of  its  section  at  that  point.  The  central  portions 
of  the  stream  move  with  greater  velocity  than  the  sides,  and  the 
top  moves  faster  than  the  bottom.  This  is  due  to  friction.  Hence, 
in  order  to  determine  the  quantity  of  water  which  flows  in  a  river 
during  any  given  time,  it  is  necessary  to  determine  the  area  of  a 
section  of  the  stream  and  the  average  velocity. 

1.  The  area  is  obtained  by  measuring  its  depth  in  different 
places  so  as  to  obtain  a  mean  depth,  and  then  multiplying  this 
into  the  width  of  the  stream. 

2.  The  mean  velocity  is  determined  by  ascertaining  the  veloci- 

From  what  point  is  the  random  greatest  ?  Where  is  the  random  equal  ? 
When  liquids  spout  through  the  air,  what  kind  of  a  curve  do  they  actually 
describe  ?  -What  is  the  velocity  of  a  stream,  in  any  part  of  its  course,  pro- 
portioned to  ?  How  is  the  area  of  a  section  of  a  stream  determined  ?  How 
is  the  velocity  ascertained  ? 


VELOCITY    OF    RIVERS. 


147 


ty  at  the  surface,  sides,  and  bottom  of  the  stream.  If  these  ve- 
locities are  3,  4,  and  5  miles  per  hour,  by  adding  them  together, 
and  dividing  by  3,  we  obtain  the  mean  velocity  in  this  case,  4 

miles  per  hour 


Fig.  115. 


These  different  velocities  may  be  ascertained 
by  noticing  the  velocity  of  light  bodies  on  the 
surface  arid  edges  of  the  stream,  but  more  ac- 
curately by  means  of  a  bent  tube,  Fig.  115. 
When  this  tube  is  placed  so  that  the  current 
flows  into  the  larger  end,  the  velocity  of  the 
stream  will  cause  the  water  to  rise  up  in  the 
tube,  and  the  height  to  which  it  rises  will  indi- 
cate the  velocity  at  the  point  where  it  is  insert- 
ed. The  velocity  is  determined  from  the  height 
to  which  the  liquid  rises,  on  the  principle  that 
a  body  projected  upward  with  the  velocity  it 
has  acquired  in  falling  through  a  given  space, 
will  rise  to  the  point  from  which  it  fell ;  and, 
if  we  know  the  height  to  which  it  rises  under 
the  influence  of  gravity,  we  may  determine  its  velocity.  Thus, 
if  the  water  rise  in  the  tube  16  feet,  then  the  velocity  of  the 
stream  is  32  feet  per  second  ;  for  a  body  projected  upward  with  a 
velocity  of  32  feet  per  second  would  rise  to  the  height  of  16  feet. 
Having  obtained  the  mean  velocity  in  feet,  this  quantity  mul- 
tiplied into  the  area  of  the  section  will  give  the  number  of  cubic 
feet  of  water  which  flows  in  the  river  during  the  given  time. 
Thus,  if  the  area  of  a  section  of  a  stream  is  200  square  feet,  and 
the  velocity  4  miles,  or  21,120  feet  per  hour,  the  quantity  dis- 
charged in  one  hour  will  be  200  times  21,120,  or  4,224,000  cu- 
bic feet. 

3.  The  velocity  of  rivers  is  greatly  retarded*  not  only  by  the 
friction  on  their  sides  and  bottoms,  but  also  by  their  irregular 
and  ivinding  course.  If  the  water  in  its  descent  observed  the 
laws  of  solid  bodies  falling  down  inclined  planes,  its  velocity,  con- 
stantly increasing  from  the  source  to  the  outlet,  would  become  so 
great  as  to  sweep  along  every  thing  in  its  course ;  but  a  fall  of 
3  inches  per  mile  is  said  to  give  a  velocity  of  only  3  miles  in  an 


How  is  the  quantity  of  water  flowing  in  any  river  determined  f 


148  NATURAL    PHILOSOPHY. 

hour.  A  fall  of  3  feet  per  mile  gives  the  velocity  of  a  torrent. 
Many  rivers,  as  the  Ganges  and  Magdalena,  fall  not  more  than 
500  feet  in  a  thousand  miles,  and  hence  their  progress  is  very 
slow.  A  descent  of  y1^ th  of  an  inch  per  mile  is  the  least  inclina- 
tion which  will  give  motion  to  water. 

PROBLEMS. 

1.  The  Mississippi  River,  at  a  certain  point,  is  500  feet  wide, 
and  the  depth,  taken  at  six  different  parts  of  the  stream,  10,  15, 
20,  30,  25,  and  8  feet.     What  is  the  area  of  the  section  ? 

Ans.  9000  square  feet. 

2.  The  velocity  at  the  bottom  and  sides  was  3  miles  per  hour, 
at  the  top  4,  and  at  the  center  5  miles  per  hour.    What  was  its 
mean  velocity  ? 

Ans.  4  miles  per  hour. 

3.  What  quantity  of  water  would  the  river,  on  the  above  sup- 
position, discharge  in  one  year,  or  365£  days  ? 

•   Ans.   1,666,241,280,000  cubic  feet. 

4.  On  the  supposition  that  j^-^th  part  of  the  water  in  the  above 
example  was  mud,  how  many  tons  of  mud  would  the  river  dis- 
charge if  its  specific  "gravity  was  2£  times  that  of  water  ? 

Ans.  260,350,200  tons. 

VI.  Resistance  of  Liquids  to  the  Motion  of  Bodies  immersed 
in  them. — Liquids,  as  well  as  solids,  have  the  property  of  iner- 
tia, and  bodies  moving  through  them  must  overcome  this  force, 
and  give  motion  to  their  particles.  In  other  words,  a  liquid,  as 
water,  must  resist  the  motion  of  any  solid  in  it  with  a  force  equal 
to  the  inertia  of  the  particles,  and  the  velocity  with  which  they 
are  moved.  Thus,  a  boat  passing  through  water  at  the  rate  of 
one  mile  per  hour,  meets  with  a  certain  resistance  from  the  water 
which  it  displaces.  If  it  move  two  miles  an  hour,  the  resistance 
will  be  not  twice,  but  four  times  as.  great,  and  of  course  will  re- 
quire four  times  as  much  power  ;  for,  in  the  latter  case,  the  quan- 
tity of  water  displaced  by  the  boat  in  the  same  time  will  be 
doubled,  which  will  double  the  resistance,  and  .the  velocity  with 
which  it  is  moved  will  also  be  twice  as  great.  Hence  the  re- 
Illustrate  tue  law  of  resistance  when  bodies  move  through  water. 


RESISTANCE    OF    LIQUIDS.  149 

sistance  will  be  four  times  as  great  for  two  miles  per  hour  as  for 
one.  If  the  velocity  be  increased  to  three  miles  per  hour,  then, 
the  resistance  will  be  nine  times  as  great,  since  both  the  quantity 
displaced  and  the  velocity  are  trebled. 

And  so,  if  the  velocity  be  four  miles  per  hour,  the  resistance  is 
increased  sixteen  times.  This  law  of  resistance  may  be  thus  ex- 
hibited :  if  we  take  the  numbers  1,  2,  3,  4,  5,  6,  7,  8,  9,  10,  to 
represent  the  velocities  with  which  any  body  moves  through  wa- 
ter, we  shall  find  the  resistance  to  be  as  the  numbers  1,4,  9,  16, 
25,  36,  49,  64,  81,  100. 

1 .  That  is,  the  force  of  resistance  increases  as  the  square  of 
the  velocity. 

Hence,  if  it  required  the  force  of  one  engine  to  drive  a  vessel 
one  mile  per  hour,  it  will  require  a  hundred  such  engines  to  pro- 
pel it  ten  miles  per  hour.  In  fact,  it  requires  rather  more  force 
than  is  indicated  by  the  above  law,  especially  when  the  motion 
becomes  very  rapid,  owing  to  the  diminution  of  the  pressure  upon, 
the  vessel's  stern.  This  pressure  is  equal  to  that  on  the  prow 
when  the  vessel  is  at  rest ;  but  as  soon  as  it  begins  to  move,  the 
water  is  parted  and  thrown  each  way  from  the  vessel's  sides,  so 
that  the  pressure  is  removed  from  the  stern ;  and  hence  this 
pressure  must  be  supplied  by  the  force  of  the  steam  or  the  wind. 
The  observance  of  this  is  very  important  in  steam  navigation. 

It  is  evident  that  the  law  of  resistance  must  be  the  same  if 
the  solid  is  at  rest  and  the  liquid  in  motion.  Thus,  a  vessel  at 
anchor,  when  the  tide  or  currents  are  running  past  her,  must  bear 
a  strain  upon  her  cable  in  proportion  to  the  square  of  the  velocity. 
Hence  it  will  require  four  times  the  strength  of  cable  to  fyold  a 
vessel  against  a  tide  moving  two  miles  per  hour  that  it  would 
if  moving  one  mile  per  hour,  for  the  reason  that^  twice  as  many 
particles  strike  the  vessel  in  the  same  time ;  and,  as  they  are 
moving  twice  as  fast,  they  strike  it  with  double  the  force. 

2.  Limit  of  Velocity. — It  is  obvious  from  the  above  laws  that 
there  must  be  a  limit  to  the  velocity  with  which  a  solid  may  be 
forced  through  a  liquid;  20,  or,  at  most,  25  miles  per  hour,  is 
the  highest  velocity  which  can  possibly  be  given  to  a  steam  ves- 

What  limit  is  there  to  the  velocity  of  a  body  moving  tiu-auqrh  a  liquid? 


150  NATURAL    PHILOSOPHY. 

sel ;  beyond  these  rates  the  resistance  becomes  so  great  that  no 
mechanical  powers  can  be  constructed  to  overcome  it,  or  increase 
the  speed.  A  force  requisite  4o  propel  a  vessel  15  miles  per  hour 
would  have  to  be  doubled  to  give  a  velocity  of  20  miles  per  hour, 
and  to  be  increased  eight  times  to  move  the  vessel  40  miles  per 
hour.  In  this  case  no  material  would  be  sufficient  to  sustain  the 
shock  of  the  resistance,  even  if  the  force  could  be  applied. 

3.  Influence  of  the  Form  upon  the  Degree  of  Resistance. — It 
would  seem,  from  a  slight  examination  of  the  subject,  that  if  a 
solid  removed  a  given  number  of  particles  of  water  to  a  <given 
distance,  that  the  resistance  would  be  the  same  whatever  the 
form  of  the  solid  ;  but  a  closer  examination  shows  that  a  concave 
surface  moving  through  water  is  most  resisted,  because  the  water 
is  not  only  parted  and  thrown  off  laterally,  but  a  portion  of  it  is 
carried  forward  in  the  direction  in  which  the  body  moves.  A 
flat  surface  presents  greater  resistance  than  a  convex  or  wedge- 
shaped  surface,  because,  though  it  moves  the  particles  to  the 
same  distance  laterally,  it  does  it  in  much  less  time,  or  it  imparts 
to  the  water  displaced  a  greater  velocity  than  a  round  or  wedge- 
shaped  surface ;  and  hence  we  find  that  the  inhabitants  of  the 
water,  as  fish,  have  such  a  form  as  to  offer  the  least  resistance  to  it. 

On  the  same  principle  ships  and  boats  are  constructed.  The 
form  of  the  stern  is  as  important  as  that  of  the  prow,  and  it  is  a 
very  important  problem  in  naval  architecture  to  determine  the 
proportions  to  be  given  to  a  vessel  in  order  that  it  may  meet 
with  the  least  resistance  from  the  water. 

Very  large  bodies  are  not  resisted  in  proportion  to  their  weight 
so  much  as  small  ones,  simply  on  the  principle  that  the  surfaces 
of  bodies  do  not  increase  in  proportion  to  their  quantity  of  matter. 
The  surfaces  o|  solids  are  as  the  squares  of  their  sides,  but  their 
quantity  of  matter  increases  as  the  cubes  of  their  sides.  Thus,  a 
solid,  as  a  cube,  whose  side  is  two  feet  in  length,  has  only  four 
times  the  surface  of  one  that  is  one  foot,  but  it  is  eight  times  as 
heavy. 

What  is  the  practical  difficulty  in  propelling  a  steam  vessel  25  or  30  miles 
an  hour?  What  influence  has  the  form  of  the  body  upon  the  degree  of 
resistance  ?  Do  bodies  meet  with  resistance  in  passing  through  liquids  in 
proportion  to  their  weight? 


MOTIVE  POWER  OF  WATER.  151 

The  motions  of  liquids  through  liquids  observe  the  same  laws 
as  solids,  and  meet  with  similar  resistance  ;  though,  in  conse- 
quence of  the  peculiar  properties  of  a  liquid,  when  a  river  dis- 
charges itself  into  the  ocean,  or  when  the  tide  sets  up  rivers,  the 
currents  are  preserved  nearly  distinct  for  a  considerable  distance, 
and  when  they  meet  they  occupy  different  sides  of  the  channel, 
and  pass  by  each  other ;  or  if  fresh  water,  as  that  of  a  river,  is 
discharged  into  salt  water,  it  flows  over  the  current  it  may  meet, 
in  which  cases  the  law  of  resistance  must  be  somewhat  modified 
Waves. — Waves  in  the  ocean  are  produced  by  the  action  of 
the  air  upon  its  surface,  and  the  constant  tendency  of  the  water 
to  return  to  a  level  condition ;  but  their  mode  of  production  will  be 
better  understood  after  attending  to  the  subject  of  Undulations, 
VII.  Water  as  a  Motive  Power. — The  force  of  water  is  em- 
ployed to  move  machinery,  and  this  is  one  of  its  most  important 
practical  uses.  This  is  effected  by  means  of  water  wheels,  which 
are  turned  by  the  force  of  the  stream.  Water  wheels  are  either 
vertical  or  horizontal.  The  principal  kinds  of  vertical  water 
wheels  are  the  overshot,  the  undershot,  and  the  middleshot,  or 
breast  wheel. 

!.  The  Overshot  Wheel  re- 
volves on  a  horizontal  axis,  and 
receives  the  water  into  cells,  or 
buckets,  placed  in  the  circum- 
ference, Fig.  116.  The  weight 
of  the  water  turns  the  wheel. 
This  kind  of  wheel  is  used  where 
the  fall  is  very  great  and  the 
quantity  of  water  small,  as  is 
often  the  case  in  mountain  streams.  These  wheels  are  made 
large,  and  have  a  slow  motion,  but  are  capable  of  exerting  great 
power,  so  that  a  small  quantity  of  water  may  be  made  to  set  in 
motion  very  ponderous  machinery.  As  the  water  acts  by  its 
weight,  and  is  applied  at  the  ends  of  a  series  of  levers,  the  power 
of  the  wheel  may  be  increased  by  simply  increasing  its  diameter. 
It  will  be  seen  that  a  wheel  20  or  30  feet  in  diameter,  with  a 
few  pounds  of  water  upon  its  circumference,  becomes  a  very  ef- 
fective mechanical  power. 

What  is  the  law  when  liquids  pass  through  liquids  ?     Describe  the  dif- 
ferent kinds  of  water  wheels.     How  is  the  overshot  wheel  constructed  ? 


152  NATURAL.    PHILOSOPHY. 

2.  Undershot  Wheels  have  ftoat-boards  Fi?-}Y!- 
instead  of  cells,  and  are  turned  by  the  force 

of  the  running  water  against  the  floats,  Fig. 

117.     This  kind  of  wheel  is  used  where 

there  is  a  large  quantity  of  water,  and  the 

iall  but  slight.     As  the  stream  strikes  the 

float,  it  imparts  its  motion  to  it,  so  that  it 

loses  a  portion  of  its  velocity.     Generally 

never  more  than  half  the  force  of  the  stream 

is  imparted  to  the  wheel  when  the  water  strikes  the  float  at  right 

angles ;  but  Pancelet  has  constructed  a  curved  float,  so  that  an 

increase  of  power  is  gained,  the  whole  effect  being  equal  to  two 

thirds  of  the  force  of  the  stream. 

3.  The  Middleshot  Wheel,  Fig.  118,  also  consists  of  a  drum, 
with  float-boards,  and  is  a  Fig  1]g 

kind  of  medium  between 
the  overshot  and  undershot 
wheel,  the  force  of  the 
stream  being  applied  at  a 
point  between  the  highest 
and  lowest  points  in  the 
circumference.  Hence  the 
term  middleshot,  or  breast. 

Horizontal  Wheels  revolve  on  an  upright  axis,  and  those 
which  have  been  rendered  most  practicable  were  invented  by 
Fourneyron,  and  called  turbines.  They  are  used  where  the  fall 
is  considerable,  or  where  the  wheel  is  required  to  move  under 
water. 

A  modification  of  Seigner's  water  wheel  has  been  made  by 
Althans,  which  remedies  the  practical  difficulty  arising  from  the 
weight  of  the  water  in  the  cylinder,  and  its  consequent  pressure 
upon  the  lower  pivot  of  the  axis.  This  is  effected  by  causing 
the  water  to  enter  the  horizontal  arms  a  b  (see  Fig.  112)  from 
below ;  and  by  curving  the  arms  in  the  form  of  the  letter  S,  a 
considerable  increase  of  power  has  been  gained  over  wheels  with 
straight  arms. 

Hydraulic  Machines. — The  principal  machines  for  lifting  wa- 
ter are  the  common  pump,  the  screw  of  Archimedes,  and  the 
chain  pump. 

Describe  the  undershot  and  breast  wheels.   What  are  horizontal  wheels  ? 


HYDRAULIC    MACHINES. 


153 


Fig.  119. 


Fig.  120. 


The  action  of  the  common  pump  will  be  better  understood  in 
connection  with  the  subject  of  Pneumatics. 

Archimedes 's  Screw. 
— This  instrument  was 
invented  by  Archimedes, 
and  consists  of  a  tube 
wound  around  a  cylin- 
der, JFSg.  119.  The  tube 
is  open  at  both  ends,  and 
is  made  to  revolve  by 
means  of  a  crank  attach- 
ed to  the  cylinder,  which 
is  placed  at  a  greater  or  less  angle  of  elevation.  The  lower  end 
of  the  tube,  as  it  is  turned,  strikes  the  water,  and  a  portion  is 
forced  into  it.  The  upward  motion  of  the  water  is  continued  by 
the  coils  of  the  tube  until  it  is  delivered  at  the  other  end. 

This  instrument  is  often  employed  to  raise  water  a  short  dis- 
tance ;  as,  in  laying  the  foundation  of  dams,  it  becomes  necessary 
to  drain  small  pits  which  become  filled  with  water. 

The  Chain  Pump  consists  of  a  series  of  small,  flat  plates, 
which  are  connected  by  joints  of  metal. 
When  this  chain  is  passed  over  a  wheel, 
the  floats,  as  the  wheel  is  turned,  rise  up 
through  a  trunk,  carrying  with  them  a 
quantity  of  water,  which  is  ejected  at  the 
spout.  There  are  many  other  machines* 
for  lifting  water,  as 

Vera's  Pump,  which  acts  by  means  of  a 
rope  passed  around  a  pulley,  and  a  wheel,  by 
which  it  is  made  to  revolve  rapidly  through 
the  water.  The  water  adheres  to  the  rope, 
and  is  lifted  to  the  required  point,  as  seen  in 
Fig.  120. 

PROBLEMS. 

1.  A  steam-boat  is  propelled  by  1  engine  at  the  rate  of  10 
miles  an  hour.  How  many  engines  of  the  same  power  would  be 
required  to  propel  it  30  miles  per  hour  ?  Ans.  9. 

*  For  a  full  description  of  hydraulic  machines,  the  student  is  referred  to 
Ewbank's  Hydraulics. 

Describe  the  screw  of  Archimedes — the  chain  pump— Vera's  pump. 
G  2 


154  NATURAL    PHILOSOPHY. 

2.  A  steam-ship  sailed  from  Boston  to  Liverpool,  a  distance  of 
3000  miles,  in  15  days,  by  means  of  a  single  engine.     What 
force  would  be  necessary  to  accomplish  the  voyage  in  10  days  ? 

Ans.  A  force  equal  to  2|  engines. 

3.  A  ship  at  anchor  was  held  by  a  cable  against  a  tide  which 
was  running  2  miles  per  hour.     What  strength  of  cable  would 
be  required  when  the  tide  runs  8  miles  per  hour  ? 

Ans.  16  cables. 

4.  An  overshot  wheel,  20  feet  in  diameter,  is  turned  by  a 
stream  which  keeps  the  buckets,  holding  15  cubic  feet,  constantly 
full  of  water.    What  force  would  be  exerted  upon  a  crank  which 
describes  a  circle  of  4  feet  in  diameter,  on  the  supposition  that 
two  thirds  of  the  force  of  the  stream  is  exerted  upon  the  wheel  ? 

Ans.  3125  Ibs. 

5.  An  undershot  wheel,  10  feet  in  diameter  and  6  feet  long,  is 
placed  at  the  side  of  a  dam  10  feet  deep.     If  the  water  press 
upon  the  floats  through  an  aperture  2  inches  high  and  6  feet 
wide,  what  power  would  be  exerted  upon  the  axle,  one  foot  in 
diameter,  <m  the  supposition  that  two  thirds  of  the  force  of  the 
stream  was  effective  to  turn  the  wheel  ? 

Ans.  4166|  Ibs. 

Agency  of  Water. — Water  is  almost  the  only  liquid  which 
exists  in  nature  in  any  considerable  quantity.  The  ocean  covers 
two  thirds  of  the  surface  of  the  earth,  and  has  been  estimated  to 
be  from  two  to  five  miles  in  depth.  In  its  circulation,  however, 
water  is  spread  over  the  whole  earth,  for  by  the  heat  of  the  sun 
it  is  constantly  rising  up  from  the  surface  of  the  ocean  in  the 
form  of  vapor,  which  is  diffused  through  the  atmosphere.  By  its 
condensation,  it  falls  in  rain  and  snow,  and  gives  rise  to  springs, 
rivers,  and  fresh-water  lakes,  through  which  it  is  again  returned 
to  the  ocean.  By  this  circulation,  and  by  the  agency  of  waves, 
the  surface  of  the  earth  has  been  repeatedly  changed  and  modi- 
fied ;  so  that  water  is  not  only  employed  in  renewing  the  face  of 
the  earth  and  clothing  it  with  beauty,  causing  it  to  "  bring  forth 

Mention  the  mode  by  which  water  is  made  to  circulate.  What  import- 
ant agency  does  it  exert? 


PNEUMATICS.  1 55 

its  fruit  in  its  season,"  but  it  has  been  chiefly  concerned,  in  con- 
nection with  fire,  in  molding  it  to  its.  present  form,  and  in  trans- 
forming its  rocky  and  barren  materials  into  the  fertile  soil  out  of 
which  man  and  his  cotemporaries  obtain  whatever  may  contrib- 
ute to  their  material  enjoyments  or  may  supply  their  physical 
wants. 


CHAPTER  V. 

PNEUMATICS. 

THE  term  Pneumatics  is  derived  from  a  Greek  word, 
the  name  of  the  air.  As  a  branch  of  Mechanics,  its  object  is  to 
investigate  the  conditions  of  the  equilibrium  and  motion  of  elas- 
tic or  aeriform  fluids. 

Aeriform  fluids  differ,  in  some  respects,  from  liquids,  and 
hence,  in  these  respects,  is  Pneumatics  distinguished  from  Hydro- 
statics. When  certain  solids  and  all  liquids  are  heated,  they  be- 
come vapors,  or  elastic  fluids,  which  differ  from  gases  in  being 
more  easily  reduced  by  cold  or  pressure  to  the  liquid  or  solid  state. 

Only  two  elastic  fluids  are  generally  treated  of  in  Natural  Phi- 
losophy :  steam,  which  is  the  vapor  of  water,  and  common  air, 
which  is  a  permanently  elastic  fluid,  because  it  has  never  been 
reduced  to  the  liquid  or  solid  state  by  cold  or  pressure. 

We  have  seen  that  the  three  forms  of  matter,  solid,  liquid, 
and  gaseous,  depend  upon  the  relative  intensity  of  cohesion  and 
caloric.  Caloric  always  pervades  the  particles  of  bodies,  and 
overcomes,  to  a  greater  or  less  extent,  the  force  of  cohesion.  The 
latter  power  is  predominant  in  solids,  nearly  in  equilibrium  with 
caloric  in  liquids,  and  entirely  destroyed  in  gases,  the  particles 
being  removed,  in  the  last,  beyond  the  reach  of  their  mutual  at- 
traction. 

Gases  differ  from  both  solids  and  liquids  in  the  fact  that,  when 
heated,  they  are  equally  expanded  by  equal  additions  of  heat. 

Meaning  of  Pneumatics.    What  is  the  distinction  between  aeriform  fluids 

at  two  aeriform  fluids  are  in- 
gases differ  from  solids  and 


ea  .  s     e     s 

and  liquids  ?  between  vapors  and  gases  ?    What  two  aeriform  fluids  are  in- 
vestigated in  Natural*  Philosophy  ?     How  do 


liquids? 


156  NATURAL    PHILOSOPHY. 

We  propose  to  treat,  in  the  first  place,  of  the  properties  of  air> 
and  then  of  the  atmosphere,  or  that  gaseous  fluid  which  sur- 
rounds the  earth,  and  extends  to  the  distance  of  forty  or  fifty  miles 
above  it. 

SECTION  I.— PROPERTIES  OF  ATMOSPHERIC  AIR. 

It  is  a  common  impression  that  the  air  does  not  possess  the 
essential  properties  of  matter. 

I.  But  the  materiality  of  air  is  proved  by  its  extension,  im- 
penetrability, weight,  inertia,  and  pressure.      These  and  other 
properties  of  air  may  be  best  exhibited  by  means  of  the  air  pump. 

II.  The  air  is  a  perfectly  elastic  fluid ;  that  is,  when  com- 
pressed, it  always  returns  to  its  original  volume  when  the  press- 
ure is  removed.      The  law  of  compressibility  and  expansibility 
is,  that  the  volume  of  a  confined  portion  of  air  is  inversely  as 
the  compressing  force. 

III.  The  air  presses  equally  in  all  directions,  downward,  up- 
ward, and  laterally.     The  amount  of  pressure  is  determined  by 
means  of  a  barometer,  and  is  about  15  Ibs.  to  a  square  inch  of 
surface,  though  ilie  pressure  varies  at  different  times  and  places 
on  the  earth's  surface. 

IV.  It  is  due  to  the  pressure  of  the  air  that  water  may  be  rais- 
ed from  wells  and  pits  by  means  of  the  lifting  pump,  syphon,  fyc. 

V.  When  air  is  compressed,  it  exerts  a  greater  or  less  force, 
which  is  due  to  its  elasticity,  and  in  this  state  may  be  employed 
as  a  mechanical  power. 

VI.  In  consequence  of  the  pressure  of  the  air  and  its  attrac- 
tion for  other  matter,  it  diffuses  itself  among  the  particles  of  sol- 
ids, liquids,  and  gases. 

VII.  Air,  like  water,  sustains  a  portion  or  the  ivhole  of  the 
weight  of  bodies  which  are  immersed  in  it. 

VIII.  It  also  opposes  a  resistance  to  bodies  passing  through  it, 
which  is  in  the  ratio  of  the  square  of  their  velocity. 

IT  is  a  very  common  impression  that  air  does  not  possess  the 
essential  properties  of  matter,  extension  and  impenetrability;  but 

What  is  the  common  opinion  respecting  atmospheric  air? 


MATERIALITY    OP    AIR. 


157 


Fig.  121. 


it  is  easy  to  show,  by  experiment  and  reference  to  various  phe- 
nomena, that  it  is  not  only  extensible  and  impenetrable,  but  that 
it  possesses  also  the  other  properties  of  matter,  such  as  attraction, 
weight,  and  the  like. 

I.  That  the  Air  is  Material  may  be  proved  by  the  following 
properties,  which  can  be  fully  illustrated  by  experiment : 

1 .  The  Air  is  Impenetrable.    This  may  be  shown 
by  placing  a  lighted  taper,  Fig.  121,  upon  a  cork  float- 
ing on  the  surface  of  a  jar  of  water,  and  inverting 
over  it  a  receiver  of  common  air.     By  pressing  the 
receiver  down,  the  taper  will  descend  apparently  be- 
neath the  water,  the  same  effect  being  produced  as 
would  be  if  the  column  of  air  in  the  receiver  were 
solid ;  that  is,  the  air  excludes  the  water  from  the 
space  it  occupies. 

If  a  solid  piston  be  fitted  to  a  cylinder  closed  at 
the  bottom,  no  force  can  press  it  to  the  bottom,  as  is 
exemplified  in  the  fire  syringe. 

2.  The  Air  is  extended  in  Space.     It  is  evident, 

from  the  above  experiments,  that  the 
particles  of  air  are  extended  ;  for,  if 
they  were  not,  it  would  be  impossible 
for  any  number  of  them  to  fill  a  por- 
tion of  space,  and  the  cork,  in  the  first 
experiment,  would  not  be  forced  down 
apparently  below  the  water.  Hence 
the  air  must  possess  the  other  essential 
property  of  matter,  extension. 

3.  The  Air  has  Weight.  That  air 
has  weight,  or  that  its  atoms  are  at- 
tracted toward  the  center  of  the  earth, 
is  shown  by  weighing  a  portion  of  air 
confined  in  a  glass  flask. 

Exp. — Take  a  glass  flask,  Fig.  122,  with 
a  stop-cock  attached,  and  with  an  air  pump 
exhaust  the  air,  and  then  weigh  it.  After 
the  readmission  of  the  air,  the  flask  will  as- 
sume the  position  shown  in  the  figure.  By 


Fig.  122. 


How  is  the  material! 
air  is  extended  ? 


teriality  of  air  proved  ?     What  experi 
that  it  has  weight  and  inertia  ? 


experiments  to  prove  that 


158  NATURAL    PHILOSOPHY. 

adding  weights  to  the  opposite  scale,  the  weight  of  the  air  may  be  determ» 
ined;  and  it  will  be  found  that  every  100  cubic  inches  will  weigh  a  little 
more  than  31  grains.  Other  gases  may  be  shown  to  have  weight  in  a  sim- 
ilar manner.  100  cubic  inches  of  hydrogen  weigh  only  2'1  grains,  while 
the  same  quantity  of  carbonic  acid  weighs  47*2  grains. 

4.  The  Air  has  Inertia.     The  materiality  of  air  is  further 
shown  by  its  inertia.     It  requires  force  to  put  it  in  motion,  or 
stop  it  when  in  motion.     This  property  of  air  may  be  made  evi- 
dent by  reference  to  the  most  familiar  phenomena. 

Ships  sail  by  the  force  of  moving  air.  Birds  fly  by  the  resist- 
ance which  the  air  offers  to  the  stroke  of  their  wings.  Light 
bodies,  as  straw  and  feathers,  and  even,  in  some  cases,  trees  and 
dwellings,  are  swept  along  or  overturned  by  currents  of  air.  Solid 
and  liquid  bodies,  moving  through  air,  meet  with  resistance,  and 
the  resistance  follows  the  same  law  as  when  solid  bodies  move 
through  water,  which  is  as  the  square  of  the  velocity ;  that  is,  a 
double  velocity  meets  with  a  quadruple  resistance  ;  for  one  body 
moving  with  twice  the  velocity  of  another,  meets  with  twice  as 
many  atoms  in  the  same  time,  and  must  move  these  with  twice 
the  velocity ;  hence  the  resistance  is  four  times  as  great.  Air  is 
about  eight  hundred  times  lighter  than  water,  and  its  inertia  and 
momentum  are  always  found  to  be  in  proportion  to  its  weight. 

5.  The  Air  is  a  Fluid.     The  fluidity  of  the  air  is  proved  by 
the  same  kind  of  facts  as  that  of  water  :  "  it  presses  and  is  pressed 
equally  in  all  directions ;"  and  if  confined,  a  pressure  or  blow  on 
one  part  presses  equally  on  every  other  part. 

From  these  and  many  other  facts,  it  is  evident  that  air  is  ma- 
terial ;  that  it  occupies  space,  is  impenetrable,  has  weight,  iner- 
tia, momentum,  and  pressure. 

For  the  purpose  of  illustrating  the  properties  of  air,  several  art- 
icles of  apparatus  are  necessary,  among  which  the  air  pump  is 
most  essential. 

The  Air  Pump. — The  air  pump  was  invented  by  Otto  de  Gue- 
ricke,  of  Magdeburg,  Germany,  in  the  year  1654.  It  was  a  sin- 
gle barrel,  with  a  piston  and  two  valves,  and  by  means  of  it  he 
exhausted  two  hollow  brass  hemispheres,  12  inches  in  diameter, 
having  the  edges  ground  so  that  when  placed  together  they  were 

What  other  proofs  of  the  materiality  of  air?     What  apparatus  most  im 
portant  for  experiments  upon  air?    Describe  the  air  pump. 


THE    AIR    PUMP. 


159 


Fig.  123. 


air-tight.  Air  pumps  are  constructed  with  double  or  with  single 
barrels.  The  latter  are  the  most  simple,  and  worked  with  the 
least  power. 

The  single  barrel  air  pump  consists 
of  a  barrel,  b,  Fig.  123,  with  a  valve 
opening  upward,  and  a  piston  connect- 
ed with  a  hollow  tube,  c,  which  passes 
up  through  the  pump  plate,  a.  The 
piston  has  a  valve  which  opens  up- 
ward, and  the  barrel  is  worked  up  and 
down  by  means  of  the  handle,  h.  The 
«j  valves  work  precisely  like  those  of  the 
common  lifting  pump  ;  but  as,  in  this 
form,  the  barrel  is  worked  up  and 
down  instead  of  the  piston,  the  valve 
is  in  the  top  of  the  barrel,  and  there- 
fore the  greatest  force  is  required  to 
press  the  barrel  down,  which  lifts  the  piston  from  the  bottom  to 
the  top  of  the  cylinder,  and  forces  out  the  air  which  flows  into 
it  from  the  receiver  when  the  barrel  is  raised  up. 

To  indicate  the  degree  of  exhaustion,  a  mercurial  gauge  is  at- 
tached. It  consists  of  a  tube,  g,  open  at  both  ends ;  the  upper 
end  opens  into  the  receiver,  and  the  lower  extends  through  the 
pump  frame  and  dips  into  a  cup  of  mercury. 

When  a  receiver  is  placed  upon  the  pump  plate,  a,  and  the  air 
exhausted,  the  tube  is  also  exhausted,  and  the  pressure  of  the  air 
on  the  surface  of  the  mercury  in  the  cup  forces  it  up  the  tube, 
and  the  height  to  which  it  rises  will  indicate  the  degree  of  ex- 
haustion. 

The  law  of  exhaustion  with  each  stroke  of  the  piston  is 
readily  deduced  from  a  knowledge  of  the  capacity  of  the  barrel 
and  of  the  receiver. 

Thus,  if  the  capacity  of  the  receiver  is  equal  to  that  of  the 
barrel,  then,  when  the  barrel  is  raised,  the  air  will  expand  and 
fill  it,  so  that  the  quantity  in  the  barrel  will  be  half  of  the  whole. 
When  the  barrel  is  forced  down,  this  half  will  be  forced  out,  leav- 
ing half  of  the  original  quantity  in  the  receiver.  When  the  bar- 
rel is  raised  again,  the  air  in  the  receiver  will  expand  and  fill  the 


What  is  the  law  of  exhaustion  in  the  air  pump  when  the  capacity  of  the 
receiver  is  equal  to  that  of  the  barrel  ? 


160  NATURAL    PHILOSOPHY. 

barrel,  which  will  then  contain  \  of  \  =  \  of  the  original  quan- 
tity. This  will  be  expelled  by  the  second  stroke,  leaving  one 
quarter  in  the  receiver.  The  third  stroke  will  halve  this  quan- 
tity* expelling  one  eighth,  and  leaving  one  eighth  of  the  original 
quantity  in  the  receiver.  That  is,  each  stroke  will  expel  half  of 
the  quantity  of  air  which  remains,  and  hence  the  whole  can  never 
be  exhausted  from  the  receiver.  It  will  be  seen  by  examining 
the  portions  expelled  by  several  successive  strokes,  that  they  form 
the  series  £,  |,  £,  TL.  These  numbers  constitute  a  geometrical 
series  whose  ratio  is  £.  Such  a  series  will  never  terminate. 
Hence  the  rate  of  exJiaustion  proceeds  in  a  geometrical  ratio. 

If  the  receiver  is  five  or  ten  times  the  capacity  of  the  barrel, 
the  same  law  may  be  deduced  ;  only  the  series  will  be  different, 
and  the  greater  the  capacity  of  the  receiver  in  proportion  to  that 
of  the  barrel,  the  slower  will  the  exhaustion  proceed.  Thus,  in 
the  above  case,  five  strokes  of  the  piston  will  expel  |i,  or  nearly 
the  whole  of  the  original  quantity  in  the  receiver  ;  but  if  the  re- 
ceiver were  nine  times  the  capacity  of  the  barrel,  then  the  series 
would  be  TL,  T2-o-,  T££o-,  &c.,  and  five  strokes  of  the  piston  would 
expel  only  i-Y^W*  or  IGSS  than  half  of  the  original  quantity ; 
hence  the  most  perfect  exhaustion  is  produced  when  the  receiver 
is  small,  and  the  barrel  of  the  pump  large  ;  hence,  also,  the  ad- 
vantage of  pumps  with  large  barrels. 

Prob.  1 .  The  barrel  of  an  air  pump  contains  9  cubic  inches  of 
air,  and  a  receiver  placed  on  the  plate  contains  81  cubic  inches. 
What  quantity  of  the  air  would  be  expelled  by  1 0  strokes  of  the 
piston  ? 

2.  A  receiver,  containing  12  cubic  inches  of  air,  contained  a 
quantity  equal  to  3  cubic  inches  after  2  strokes  of  the  piston. 
What  was  the  size  of  the  barrel  ? 

Ans.  12  cubic  inches. 

By  means  of  the  air  pump  and  other  apparatus  to  be  described, 
we  proceed  to  illustrate  and  prove  the  principal  properties  of  air. 

II.  Elasticity  of  the  Air. — 1 .  The  air  is  a  permanently  and 
'perfectly  elastic  fluid.    By  the  elasticity  of  the  air  is  meant  that 
What  is  said  of  the  elasticity  of  the  air  ? 


ELASTICITY    OF    THE    AIR. 


161 


Fig.  124. 


Fig.  125. 


power  which  a  compressed  portion  of  it  has  to  spring  back  to  its 
original  dimensions,  or  to  expand  when  the  pressure  is  removed. 
It  is  perfectly  and  permanently  elastic  ;  for  if  a  portion  of  air  be 
compressed  for  any  length  of  time  whatsoever,  upon  the  removal 
of  the  pressure  it  will  regain  its  original  volume. 

The  elasticity  of  the  air  may  be  illustrated  by  many  ex- 
periments. 

Exp. — Thus,  if  we  take  a  tube  with  a  bulb  at  the  end,  and  invert 
it  in  some  coloi-ed  liquid,  Fig.  124,  on  cooling  the  bulb  the  air  will 
contract,  and  the  heat  of  the  hand  will  expand  it.  These  contrac- 
tions and  expansions  are  indicated  by  the  rise  and  fall  of  the  liquid 
in  the  stem  of  the  tube.  This  instrument  is  therefore  used  as  a  ther- 
mometer, under  the  name  of  the  Air  Thermometer. 

Exp. — Fill  a  bladder  with  air,  and  compress  it ;  when  the  press- 
ure is  removed,  it  will  return  to  its  original  volume. 

Exp. — Place  a  portion  of  air  confined  in  an  India  rubber  bag  in 
a  receiver,  Fig.  125.  Upon  exhausting  the  air  around  the  bag, 
that  is,  removing  the  pressure  from  the  exterior  surface  of  the 
bag,  the  air  within  will  expand  and  fill  the  bag  full.  Upon  the 
read  mission  of  the  surrounding  air,  the  bag  will  collapse  and  re 
turn  to  its  original  dimensions. 

Exp. — If  some  soap  bubbles  be  placed  under  the  receiver 
and  the  air  exhausted,  they  will  increase  rapidly,  owing  to  the 
expansion  of  the  air  which  they  contain. 

2.  Force  exerted  by  the  Elasticity  of  Air. — It  will 
be  noticed  that  the  elasticity  of  the  air,  when  the 
pressure  is  femoved,  is  capable  of  exerting  consider- 
able force.  This  fact  may  be  illustrated  by  many 
beautiful  experiments. 

Exp. — Fill  a  small  bolt-head  with  water,  leaving  a  small 
bubble  of  air,  Fig.  126,  and  invert  it  in  a  vessel  of  water.     If 
this  be  placed  under  the  air  pump  receiver  and  the  air  ex- 
hausted, the  bubble  will  expand  and  drive  the  water  en- 
tirely out  of  the  ball.     On  admitting  the  air,  the  water 
will  be  forced  back  again.     In  this  case,  however,  the 
force  of  gravity  aids  the  elasticity  of  the  air. 

Exp. — There  is  a  small  portion  of  air  in  the  large  end 
of  an  egg,  and  by  breaking  the  small  end  and  placing  the 
egg  under  the  exhausted  receiver,  the  air  will  expand 
and  drive  the  egg  out  of  its  shell,  Fig.  127.  On  admit- 
ting the  air,  it  will  be  forced  back  again. 

The  force  of  expansion,  when  the  pressure  is 
removed,  is  sufficient  to  break  thin  glass  ves- 


Fiff.  126. 


Fig.VZJ. 


What  experiments  to  prove  the  elasticity  of  air  ?     Illustrate  the  force  of 
the  elasticity  of  the  air  when  the  pressure  is  removed. 


162 


NATURAL    PHILOSOPHY. 


Exp.-Pla.ee  a  square  glass  jar,  c,  Fig.  128,  tightly  closed,       *V- 128- 
under  the  receiver  of  an  air  pump,  a.     On  exhausting,  the 
elasticity  of  the  confined  air  will  be  sufficient  to  burst  the  ves- 
sel.    A  gauze  wire  should  be  placed  over  the  jar  b,  to  pre- 
vent the  glass  from  injuring  the  pump  plate. 

Exp. — Take  a  jar  of  water,  in  which  place  a  ball  of  glass ; 
fill  it  with  water  except  a  small  bubble  of  air  in  the  top,  suf- 
ficient to  render  it  a  very  little  lighter  than  water,  and  tie 
over  the  jar  a  piece  of  India  rubber  cloth.  If  pressure  is  ap- 
plied to  the  top  by  the  finger,  it  will  condense  the  air  in  the 
glass  ball,  and  cause  it  to  sink.  On  removing  the  pressure,  it 
will  rise.  This  is  a  beautiful  toy,  Fig.  129,  called  the 

Hydrostatic  Balloon. — If  the  ball  is  made  a  little 
heavier  than  the  water,  so  as  to  remain  at  the  bottom 
of  the  jar,  and  the  cloth  removed,  on  placing  the  whole 
under  the  receiver  and  exhausting  the  air,  the  bubble 
in  the  ball  will  expand,  drive  the  water  out,  and  the 
ball  will  rise  to  the  surface.  On  admitting  the  air,  the 
balloon  will  sink,  because  the  air  within  is  condensed, 
and  the  water,  being  forced  in,  renders  the  balloon  spe- 
cifically heavier  than  water. 

The  elasticity  of  the  air  may  be  employed  to  pro- 
duce a  beautiful  jet  of  water,  by  using  an  instrument 
called 

The  Transferrer,  Fig.  130,  which  consists  of  p^.  i30. 
two  glass  globes,  a  b,  permanently  connected  to- 
gether. The  upper  ball,  b,  is  open  at  the  top,  and 
a  flask,  c,  is  inverted  over  a  jet  pipe,  d  e,  which 
extends  to  the  bottom  of  a.  The  lower  bulb,  a,  is 
partially  filled  with  water,  having  a  small  quan- 
tity of  air  confined  in  its  upper  portion.  Now,  by 
placing  a  receiver  over  the  whole  and  exhausting, 
the  air  expands  in  a,  and  forces  the  water  up 
through  the  tube  into  the  second  vessel,  b,  and 
when  the  air  is  admitted,  the  water  is  forced  by  the  pressure  of 
the  air  into  the  flask  c.  By  this  process  the  liquid  is  transferred 
from  the  lower  to  the  upper  vessel. 

3.  Law  of  Expansibility  and  Compressibility  of  Air. — The 
general  law  of  the  compressibility  and  expansibility  of  the  air 
may  be  thus  stated  : 

Describe  the  experiment  with  square  bottle.  Describe  the  hydrostatic 
balloon.  How  does  this  experiment  illustrate  the  force  of  elasticity  ?  De- 
scribe the  transferred  What  is  the  law  of  the  compressibility  and  expansi- 
bility of  air? 


PRESSURE    OF    THE    AIR.  163 

The  volume  of  a  confined  portion  or  given  iveight  of  air  is 
inversely  as  the  compressing  force,  or  the  greater  the  force  the 
less  the  volume,  and  the  less  the  force  the  greater  the  volume. 
F^.  i3i.  This  law  may  be  illustrated  by  means  of  a  bent  glass 
tube,  Fig.  131,  closed  at  b.  By  pouring  a  little  mercury 
into  the  tube,  a,  sufficient  to  insulate  the  air  in  d,  the  press- 
ure upon  it  will  be  equal  to  that  of  the  atmosphere,  which 
is  15  Ibs.  to  the  square  inch.  If  now  the  tube  be  filled 
to  the  height  of  30  inches  with  mercury,  which  is  also 
equal  to  a  pressure  of  15  Ibs.  to  the  square  inch,  the  vol- 
ume  of  air  in  d  will  be  reduced  just  one  half,  or  it  will  oc- 
Hc  cupy  but  one  half  the  space,  and  the  mercury  will  rise  to  c. 
m  Hence  double  the  pressure  will  halve  the  volume.  Four 
times  the  pressure  will  diminish  the  volume  to  one  quarter  its 
former  bulk.  On  the  other  hand,  if  the  pressure  be  removed, 
one  half  the  pressure  will  double  the  volume,  or  one  quarter  the 
pressure  will  render  the  volume  four  times  as  large.  The  air 
becomes  denser  as  the  pressure  is  increased,  or  both  the  density 
and  elasticity  of  the  air  are  always  as  the  pressure.  We  may 
account  for  this  property  of  air  by  the  fact  that  the  atoms  of 
which  it  is  composed  are  surrounded  by  a  resisting  and  expand- 
ing power,  and  hence,  when  the  pressure  is  removed,  they  tend  to 
separate  further  and  further  from  each  other. 

For  the  purpose  of  condensing  the  air,  a  machine  called 

132  T^  Condensing  Pump  is  employed,  Fig.  132. 

This  instrument  is  similar  to  the  exhausting  pump, 
with  this  exception,  the  piston  f  contains  no  valve. 
The  valve  in  the  barrel  at  d  opens  downward,  and 
the  air  is  forced  in  by  the  piston,  but  is  prevented  from 
return  ing  by  its  elasticity,  which  closes  the  valve. 

III.  Pressure  of  the  Air. — The  pressure  of  the 
air  is  caused  by  its  weight.  The  intensity  of  this 
force,  and  the  fact  that  it  operates  equally  in  all  di- 
rections, may  be  shown  by  the  following  experiments. 

1.  Downward  Pressure  of  the  Air. — The  down- 
ward pressure  of  the  air  results  from  its  weight. 

Exp. — Place  the  receiver  upon  the  plate  of  the  pump,  and 

Illustrate  this  law.     Describe  the  condensing  pump.     What  is  the  cause 
of  the  pressure  of  the  air  1    Illustrate  its  pressure. 


164  NATURAL    PHILOSOPHY. 

exhaust  the  air  from  it ;  the  downward  pressure  will  be  indicated  by  the  firm- 
ness with  which  the  receiver  is  held  to  the  plate.  If  the  receiver  is  large, 
the  force  is  sufficient  to  lift  a  pump  weighing  two  or  three  hundred  pounds. 

Exp. — Take  a  small  receiver,  open  at  both  ends,  F-     133 

Fig.  133,  called  a  hand  glass,  and  place  the  hand  over 
the  upper  end;  on  exhausting  the  air,  the  pressure 
will  be  so  great  that  the  hand  can  not  be  lifted  with- 
out great  effort. 

This  is  the  principle-  of  cupping,  for  which 
purpose  the  skin  is  first  slightly  cut,  and  a  small 
receiver  is  placed  over  that  part  from  which  it 
is  intended  to  draw  blood.     Upon  exhausting*  the  air,  the  press- 
ure upon  the  surrounding  part  is  sufficient  to  force  the 
blood  from  the  veins, 

Exp. — Tie  a  bladder  over  the  open  end  of  a  receiver,  Fig.  134, 
and  exhaust  the  air ;  the  bladder  will  be  bent  inward,  and,  if 
struck  when  tensely  stretched,  will  burst  with  a  loud  report. 

The  Sucker. — The  pressure  of  the  air  is  often  illus- 
trated by  a  circular  piece  of  leather  with  a  string  pass-     Fig.  135. 
ed  through  the  center,  A,  Fig.  135.     When  this  is 
moistened  and  pressed  down  on  any  smooth  surface,  a 
weight  of  many  pounds  may  be  raised  by  the  string 
in  the  center,  in  consequence  of  the  pressure  of  the  air 
upon  its  surface.     Boys  often  use  this  to  lift  smooth 
stones  and  drag  them  along. 

Insects  are  enabled  to  walk  upon  the  ceiling  of  a  room  be- 
cause their  feet  are  formed  like  the  sucker,  and  the  upward 
pressure  of  the  air  holds  them  firmly  to  the  ceiling.  Animals 
drink  and  draw  their  milk  by  forming  a  vacuum  with  their  lips, 
and  the  atmosphere  forces  the  liquid  into  their  mouths.  What 
is  called  suction  is  nothing  but  the  pressure  of  the  air  exerted 
upon  the  surface  of  a  liquid,  forcing  it  into  a  partial  vacuum, 
which  is  formed  by  the  mouth  or  by  some  other  mechanism. 

2.  The  Pressure  of  Air  in  all  directions  is  beautifully  illus- 
trated by  the  Magdeburg  Hemispheres.  These  consist  of  two 

*  The  exhaustion  in  the  case  of  cupping  is  usually  made  by  simply  burn- 
ing a  little  alcohol  in  the  cup,  which  consumes  the  air  in  it,  and  then  in- 
verting it  suddenly  over  the  part  from  which  it  may  be  desirable  to  force 
out  the  blood. 

What  is  the  principle  of  cupping  ?  Describe  the  sucker.  What  experi- 
ments illustrate  the  pressure  of  the  air  in  all  directions. 


PRESSURE    OF    THE    AIR. 


165 


Fig.  136.  hemispheres,  Fig.  136,  and  accu- 

rately fitted  to  each  other.     If  they 
are  6  inches  in  diameter,   on  ex- 
hausting the  air,  they  will  be  held 
,,  A.- ,  together  so  firmly  that  the  strength 

of  two  men  can  not  pull  them  asunder.  In  this  case  the  press- 
ure must  be  in  all  directions ;  there  is  an  upward  and  lateral 
as  well  as  downward  pressure. 

3.  The  ~Upward  Pressure  of  the  Air  may  be  shown  by  filling 
a  wine-glass  with  water,  and  laying  a  paper  over  the  open  end  in. 
contact  with  the  water.  It  may  then  be  inverted,  and  the  up- 
ward pressure  of  the  air  will  prevent  the  escape  of  the  water. 

If  a  tight  vessel  be  filled  with  water  and  an  aperture  made  in 
the  bottom,  the  water  will  not  run  out  because  of  the  upward 
pressure  of  the  air ;  but,  by  making  a  small  hole 
in  the  top,  it  will  immediately  flow  ;  hence  the 
reason  that  a  cask  of  beer  or  cider  can  not  be 
emptied  from  the  faucet  unless  a  vent  hole  be 
made  in  the  top. 

This  fact,  as  well  as  the  force  of  the  upward 
pressure,  may  be  illustrated  in  a  more  striking 
manner  by  the 

Weight  Lifter. — This  consists  of  a  glass 
cylinder,  b,  Fig.  137,  closed  at  the  top,  with  a 
piston,  a,  fitted  to  it. 

Exp. — By  means  of  a  tube  from  c,  connected  with 
no    the  air  pump,  exhaust  the  air  from  b,  and  the  upward  pressure  of 
.  138.    ^  ajr  beiow  a  will  force  the  piston  up  with  an  attached  weight. 
If  the  cylinder  is  six  inches  in  diameter,  it  will  raise  more  than 
two  hundred  pounds. 

4.  Amount  of  Atmospheric  Pressure. — The  amount 
of  atmospheric  pressure  is  determined  by  counterbalanc- 
ing the  pressure  of  the  air  by  some  liquid,  as  mercury 
or  water,  and  then  ascertaining  the  weight  of  the  liquid. 
Thus  :  If  we  take  a  glass  tube,  a  b,  Fig.  138,  some  three 
feet  in  length,  closed  at  one  end,  and,  having  filled  it  with 
c  mercury,  invert  it  in  a  vessel,  c,  containing  the  same  liq- 
uid, the  pressure  on  the  outer  surface  of  the  mercury  in 
the  cup  will  sustain  the  mercury  in  the  tube  to  the  height  of  30 
inches.  That  it  is  the  pressure  of  the  air  which  sustains  the  col- 
umn of  mercury  can  be  proved 

Describe  the  weight  lifter.     What  does  it  prove  ? 


Fig.  137. 

&    {^    ^>j      ' 

b 

|_^ 

:     LJZ_^, 

.^ 

LW 

106 


NATURAL    PHILOSOPHY. 


Fig.UO. 


By  placing  the  tube  in  a  tall  glass  receiver,  Fig.  139,  J'fr  139. 
and  exhausting  the  air,  the  mercury  will  gradually  sink 
as  the  exhaustion  proceeds,  and  will  finally  be  nearly 
emptied  from  the  tube.  Upon  the  readmission  of  the 
air,  it  will  rise  to  its  former  height.  If  water  were  used 
instead  of  mercury,  the  pressure  would  sustain  a  column 
about  34  feet  in  height. 

By  this  experiment  we  can  determine, 

5.  The  Weight  of  the  Atmosphere,  or  the  amount  of 
pressure  on  any  given  surface. — If  the  tube  contain  one 
square  inch  of  surface,  the  weight  of  a  column  of  mercu- 
ry thirty  inches  in  height  will  be  fifteen  pounds ;  and 
as  the  atmosphere  sustains  or  balances  this  weight,  it  must 
also  press  with  a  force  of  fifteen  pounds  on  every  square 
inch  of  surface.     This  force  is  sufficient  to  press  upon  a 
man's  body  with  a  weight  of  fifteen  tons  !    The  reason  we 
do  not  feel  it  is,  that  there  is  air  within  the  body,  so  that 
the  inner  and  outer  pressure  is  equalized.     If,  however,  it 
be  removed  from  one  part,  this  enormous  pressure  will  im- 
mediately be  realized.     The  amount  of  atmospheric  press- 
ure is  measured  by  means  of  the 

Barometer. — A  tube  filled  with  mercury,  as  in  the  above 
experiment,  and  supplied  with  a  scale  and  some  other  fix- 
tures/is called  a  Barometer,  Fig.  140.  The  uses  of  this  in- 
strument are  to  determine  not  only  the  actual  weight  of  the 
air,  but  also  to  indicate  its  variations  in  pressure ;  and  as 
the  pressure  diminishes  in  ascending  above  the  level  of  the 
sea,  it  is  also  used  to  determine  the  height  of  mountains. 

It  will  be  seen  that  when  the  tube  is  filled  with  mer- 
cury and  inverted  in  a  cup  holding  the  same  liquid,  the 
mercury  will  sink  to  about  the  height  of  thirty  inches,  leav- 
ing the  upper  portion  of  the  tube  void  of  air. 

This  is  the  most  perfect  vacuum  possible,  and  is  called  V 
the  Torricellian  Vacuum,  from  the  name  of  its  Italian  inventor, 
Torricelli.  V  is  a  screw  to  raise  the  mercury  in  the  vessel  to 
the  point  where  the  scale  commences.  This  scale  extends  to 

How  is  the  amount  of  atmospheric  pressure  determined  ?  What  is  the 
pressure  of  air  on  each  square  inch  of  surface?  Describe  the  barometer. 
What  are  its  uses  ? 


VARIATION?    OP    ATMOSPHERIC    PRESSURE. 


167 


Fig.  141. 


the  upper  portion  of  the  tube,  where  it  is  graduated  to  inches  and 
tenths  of  an  inch,  and,  to  indicate  very  slight  variations,  a  verniei 
is  applied  to  the  scale,  which  carries  the  divisions  to  the  hundredth 
of  an  inch. 

The  Vernier  is  a  small  scale,  v  r,  Fig.  141, 
fitted  to  slip  up  and  down  upon  the  princi- 
pal scale,  b,  but  the  divisions  are  a  little  larg- 
er. In  the  barometer  scale  an  inch  is  divid- 
ed into  ten  parts,  but  the  divisions  of  the 
vernier  are  such  that  ten  of  them  are  equal 
to  eleven  on  the  barometer  scale,  so  that  one 
division  of  the  vernier  is  one  hundredth  larg- 
er than  a  division  on  the  barometer  scale. 
By  placing  the  two  scales  together  at  30 '2 
inches,  and  moving  the  vernier  up  until  it  is 
at  the  exact  height  of  the  mercury,  and  then 
looking  down  the  scale  to  the  fourth  division, 
it  is  opposite  to  one  of  the  divisions  of  the 
barometer  scale.  As  one  division  of  the  ver- 
nier is  T£o-th  larger  than  one  of  the  barometer 
scale,  it  has  gained  T|otns  of  an  inch,  ana 
the  mercury  stands  at  30-24  inches. 

In  Stationary  Barometers  the  mercury  is 
contained  in  an  open,  wide  basin ;  but  when  it  is  intended  for 
transportation  from  place  to  place,  the  mercury  is  sometimes  in- 
closed in  a  leather  bag,  with  a  screw  to  force  up  the  mercury  into 
the  tube  to  the  height  corresponding  with  the  commencement  of 
the  scale ;  for,  in  all  kinds  of  barometers,  the  more  mercury  there 
is  in  the  tube,  the  less  there  will  be  in  the  basin.  Such  a  barom- 
eter can  be  transported  without  any  danger  to  the  instrument 
from  the  fluid  condition  of  the  mercury.  When  it  is  mounted  in 
the  form  of  a  walking-cane,  it  is  a  convenient  instrument  for  de- 
termining the  height  of  mountains,  and  hence  is  termed  the 
Mountain  Barometer. 

6.  Variations  of  Atmospheric  Pressure. — By  means  of  the 
barometer,  the  variations  of  pressure,  at  different  times  and  in 
different  situations  on  the  earth's  surface,  may  be  accurately  as- 
certained. The  whole  amount  of  variation  of  pressure  at  the 


Describe  the  vernier — the  stationary  and  mountain  barometer, 
other  uses  of  the  barometer? 


What 


168  NATURAL    PHILOSOPbl. 

surface  of  the  ocean  is  about  three  inches — ranging  from  twenty- 
eight  to  thirty-one  inches ;  and  as  such  variations  indicate  some 
changes  in  the  atmosphere,  the  barometer  becomes  a  iveather- 
glass,  and  enables  us  to  predict,  with  tolerable  certainty,  storms, 
high  winds,  and  other  atmospherical  phenomena.  Generally, 
the  rise  of  the  mercury  indicates  fair,  and  its  fall  foul  weather. 
During  or  just  before  a  storm,  the  height  will  depend  upon  the 
position  of  the  barometer  in  relation  to  the  center  of  the  storm. 

A  high  wind  is  also  attended  or  preceded  by  a  fall  in  the  mer- 
cury. Of  course  its  rise  shows  that  the  column  of  air  at  that 
place  has  become  condensed,  and  its  fall  shows  that  the  air  is 
rarefied  by  some  atmospheric  changes,  the  cause  of  which  is  not 
fully  understood. 

At  the  level  of  the  sea  the  mean  height  of  the  barometer  is 
found  to  be  nearly  the  same,  thirty  inches ;  but  the  oscillations 
are  not  equal  for  every  degree  of  latitude.  These  variations  are 
least  in  the  tropics,  and  greatest  between  30°  and  60°  of  lati- 
tude. At  New  York  city  the  variation  of  the  barometer  is  less 
than  two  inches ;  in  London,  about  three  inches ;  while  within 
the  tropics  its  variation  rarely  exceeds  a  fourth  of  an  inch. 

These  variations  are  dependent  in  some  degree  upon  moisture 
and  temperature.  Hence  a  thermometer  is  usually  attached  to 
the  barometer,  and  the  temperature  of  the  place  where  the  ob- 
servations are  made  carefully  noted. 

There  are  also  variations  at  different  hours  of  the  day,  called 
horary  variations,  but  these  are  very  slight.  At  New  York,  by 
the  observations  of  Mr.  Redfield,  the  mean  variation  from  ten 
A.M.  to  six  P.M.  is  0'39  inches. 

In  ascending  above  the  level  of  the  sea,  the  column  of  air  be- 
comes shorter,  and  the  pressure  is  in  consequence  diminished. 
By  numerous  experiments  it  has  been  found  that  the  mercury 
sinks  about  one  tenth  of  an  inch  for  every  eighty-seven  feet  (see 
page  183).  Hence  the  utility  of  the  barometer  to  determine  the 
height  of  mountains. 

The  height  of  mountains  is  sometimes  determined  by  the  tem- 

What  variations  in  the  barometer  at  different  latitudes  ?  What  is  the  law 
of  variation  in  the  barometer  as  we  ascend  above  the  level  of  the  sea  ? 


peratures  at  wnicn  water  or  alcohol  boils  in  the  valley  and  at 
their  summits,  for  the  pressure  of  the  atmosphere  upon  the  sur-     .       . 


face  of  liquids  modifies  their  boiling  temperatures, 
the  pressure,  the  higher  the  temperature  at  which  they  boil ;  and, 
on  the  other  hand,  if  the  pressure  be  removed,  their  boiling  tem- 
peratures will  be  lowered.  Thus  water  which  boils  at  the  sur- 
face of  the  ocean  at  212°  F.,  will  boil  at  72°  F.  in  a  vacuum. 
Alcohol  will  boil  at  36°,  while  ether  boils  below  zero.  Alcohol 
and  ether,  therefore,  and  some  other  liquids,  would  not  exist  in 
the  liquid  state  at  the  ordinary  temperature  if  the  pressure  of  the 
atmosphere  were  removed,  but  would  wholly  pass  into  the  state 
of  vapor.  \ 

Now,  as  we  ascend  above  the  level  of  the  ocean,  the  pressure 
is  diminished,  and  it  is  found  that  an  ascent  of  about  550  feet 
will  lower  the  boiling  point  of  water  one  degree  ;*  and  hence,  by 
Fig.  142.  means  of  tables  constructed  for  the  purpose,  the 

height  above  the  ocean  may  be  readily  ascer- 
tained by  the  temperature  at  which  water  boils 
at  any  given  point. 

IV.  MecJianical  Pressure  of  Air  on  the 
Surface  of  Liquids. — The  pressure  of  air  on 
the  surface  of  water,  in  connection  with  its 
elasticity,  produces  many  beautiful  phenomena 
in  nature,  and  is  the  source  of  much  utility  in 
the  arts. 

Exp. — To  illustrate  the  pressure  of  air  on  liquids, 
take  a  glass  fountain  furnished  with  a  stop-cock,  Fig. 
142,  with  a  jet  pipe,  a,  passing  into  the  interior.  Ex- 
haust the  air,  and  then,  having  placed  the  lower  end 
of  the  tube  in  a  vessel  of  water,  turn  the  stop-cock. 
The  pressure  of  the  air  on  the  outer  surface  of  the  liq- 
uid will  force  the  liquid  into  the  fountain  in  a  beauti- 
ful jet  until  it  is  nearly  full. 

*  In  consequence  of  the  diminished  pressure,  water  on  high  mountains 
will  boil  at  a  temperature  so  low  that  in  some  cases  it  can  not  be  used  for 
culinary  purples.  This  is  said  to  be  the  case  at  the  monastery  of  St.  Ber- 

What  other  methods  for  ascertaining  the  height  of  mountains  ?  At  what 
rate  does  the  pressure  diminish  above  the  level  of  the  sea  ?  What  effect 
has  the  pressure  of  air  upon  liquids  ?  What  illustrations  of  the  mechanical 
pressure  of  air  on  the  surface  of  liquids  ? 

H 


170 


NATURAL    PHILOSOPHY. 


a 


Exp. — The  experiment  may  be  varied  by  placing  a  bolt-  ^g- 143. 
head,  a,  Fig.  143,  upon  the  top  of  a  receiver,  c,  with  a  pipe 
extending  into  a  vessel  of  water,  B.  On  exhausting,  the 
elasticity  of  the  air  in  a  will  cause  it  to  flow  out  through  the 
water ;  then,  by  allowing  the  air  to  flow  into  the  receiver,  it 
will  force  the  water  into  the  bulb  a.  If  the  water  is  colored 
in  thJe  experiment,  the  appearance  is  rendered  much  more 
striking  and  beautiful. 

If,  instead  of  exhausting  the  air  from  any  vessel 
before  placing  it  over  water,  it  be  filled  with  a  liquid 
heavier  than  water,  the  heavier  liquid  will  flow  out, 
and  the  atmospheric  pressure  will  force  the  water  in 
to  supply  its  place.  Thus,  if  a  small  tube  be  filled 
with  mercury  and  inverted  in  a  vessel  of  water,  the 
mercury  will  flow  out  and  the  water  will  be.  forced  in  to  supply  its 
place.  It  is  on  this  principle  that  the  slaves  in  the  West  Indies 
are  said  to  steal  rum.  They  fill  a  bottle  having  a  long  neck  with 
water,  and  insert  the  neck  in  the  bung-hole  of  the  cask ;  the 
water,  being  heavier  than  the  spirit,  falls  down,  and  its  place  is 
filled  by  the  lighter  liquid,  which  is  forced  up. 

Lifting  Pump. — The  common  pump  depends  for  its  utility 
upon  the  pressure  of  the  air,  a  vacuum  being  formed  in  the  bar- 
rel by  the  piston  as  it  is  lifted  up. 

Thus,  let  a  b,  Fig.  144,  represent  the  bar- 
rel, with  the  piston  and  valves  of  the  com- 
mon lifting  pump.  There  is  a  valve,  a,  in 
the  piston,  opening  upward,  and  one  at  b,  in 
the  lower  part  of  the  barrel,  also  opening  up- 
ward, similar  to  the  air  pump.  When  the 
piston  is  raised  by  means  of  the  handle,  a 
vacuum  is  formed  below  it  between  a  and  b, 
and  the  pressure  of  the  air  on  the  water  in 
the  vessel  below  forces  it  up  through  the  tube, 
lifts  the  valve,  and  causes  it  to  follow  the 
piston  to  the  top.  When  the  piston  descends, 
the  lower  valve  is  closed  and  the  upper  valve  opened,  so  that  the 

nard,  in  Switzerland,  where  the  monks  find  it  difficult  to  qpk  their  vege- 
tables. 

In  the  process  of  refining  sugar,  where  the  heat  may  do  injury,  the  sirup 
is  sometimes  evaporated  in  vacuo.  The  cost  of  fuel  in  this  case  is  much 
diminished. 


Describe  the  lifting  pump.     How  are  its  valves  arranged  ? 


LIFTING    AND    FORCING    PUMP.  171 

water  passes  above  the  piston.     The  next  stroke  closes  the  piston 
valve,  and  the  water  is  lifted  to  the  spout. 

The  height  of  the  lower  valve  can  not  be  more  than  thirty- 
four  feet  from  the  surface  of  the  water,  because  the  pressure  of 
the  air  is  only  sufficient  to  sustain  a  column  of  water  at  that 
height.  Practically,  the  lower  valve  must  be  at  a  point  a  little 
less  than  thirty-four  feet  from  the  surface,  in  order  that  the  wa- 
ter may  pass  through  the  valve  of  the  piston  as  it  descends. 

The  Forcing  Pump,  c  d,  Fig.  145,  differs  from  the  lifting 
pump  in  two  respects :  the  piston,  c,  is  solid,  and  when  it  passes 
down  it  closes  the  lower  valve,  d,  and  forces  the  water  through 
a  pipe  in  the  side  of  the  cylinder,  which  has  a  valve  opening 
inward.  In  some  cases  the  water  passes  into  an  air  chamber, 
e,  and  the  elasticity  of  the  air  renders  the  stream  from  the  spout 
constant. 

The  Syphon  depends  on  the  same  princi- 
pie. 

The  syphon  is' a  bent  tube,  Fig.  146,  with 
one  arm  longer  than  the  other.  If  the  tube 
be  filled  with  water,  and  the  short  arm  placed 
in  a  vessel  of  water,  A  B,  as  the  column  of 
water  in  E  D  falls  out,  the  pressure  on  the 
surface  of  the  liquid  in  the  vessel  will  press  it 
up  through  C  to  E  with  a  force  equal  to  the 
difference  of  the  weight  of  water  in  the  two 
arms  of  the  tube,  and  the  vessel  will  be  en- 
tirely  emptied. 

Tantalus's  Cup  acts  on  the  same  principle,  b  dl  Fig.  147,  is 
Fig.  147.  the  syphon  tube  contained  in  the  cup  c.  When  the  cup 
is  filled  so  as  to  cover  the  tube,  the  water  passes  up  b  and 
down  d,  and  as  the  column  in  d  is  longer  than  that  in  b, 
and  consequently  heavier,  as  it  flows  out  through  a  it 
tends  to  form  a  vacuum  in  the  tube  ;  but  this  is  prevent- 
ed by  the  pressure  of 'the  air,  which  forces  the  liquid 
through  b  until  the  cup  is  emptied. 
The  syphon  has  been  used  to  drain  pits  and  mines,  a  tube  being 
placed  in  the  bottom  of  the  pit,  and  conducted  over  the  edges 
far  enough  to  bring  the  other  end  below  that  in  the  well.  The 
syphon  is  then  filled,  and  the  water  will  flow  till  the  pit  or  mine 

How  far  from  the  surface  of  the  water  may  the  lower  valve  be  placed  ? 
Describe  the  forcing  pump — the  syphon  and  Tantalus's  cup. 


NATURAL    PHILOSOPHY. 

is  entirely  drained.  In  this  case  the  depth  is  limited  to  thirty- 
four  feet,  the  greatest  height  to  which  the  air  will  sustain  a  col- 
umn of  water. 

Intermittent  Springs  depend  upon  the  same  principle.  There 
are  some  springs  which  flow  for  a  time  and  then  cease.  This  is 
explained  hy  the  fact  that  the  water  accumulates  in  caverns  in 
the  earth  which  have  passages  in  the  rocks  from  the  source  to 
the  outlet  in  the  form  of  the  syphon.  When  these  fountains  are 
full  they  commence  flowing,  and  do  not  cease  till  their  whole 
contents  have  been  discharged.  They  are  then  dry  till  the  reser- 
voir is  again  filled,  when  they  again  begin  to  flow. 

The  mode  in  which  these  springs  are  produced  may  be  illus- 
trated by  means  of  Tantalus's  cup.  Let  the  cup  represent  the 
cavern  in  the  mountain  which  is  filled  with  water  from  the  rains, 
and  let  the  tube  d,  instead  of  passing  down  through  the  cup,  be 
carried  through  the  side  at  a  small  distance  from  the  top.  This 
tube  will  represent  the  passage  in  the  rocks  from  the  fountain. 
Now,  when  the  cup  is  filled,  the  water  will  begin  to  flow,  and 
continue  till  the  whole  is  emptied  ;  but  if  water  is  poured  into  it 
gradually,  it  will  not  begin  to  flow  again  until  it  is  full,  when  it 
will  be  emptied  a  second  time. 

V.  Force  exerted  by  Condensed  Air  upon  Solids  and  Liquids. 
— Hitherto  we  have  considered  the  force  of  the  air,  its  pressure 
and  elasticity  when  in  a  natural  state  ;  but  if  it  is  compressed 
into  a  small  compass  and  allowed  to  expend  its  force,  its  elastici- 
ty will  exert  a  far  greater  power  than  in  its  ordinary  state. 

As  air  is  perfectly  elastic,  it  is  highly  advantageous  for  us  to 
avail  ourselves  of  this  power  in  connection  with  several  engines 
used  in  the  arts.  The  condensing  force  may  be  exerted  by  a  con- 
densing pump  or  a  column  of  water.  For  experiments  on  the 
elastic  force  of  air,  we  may  employ  the 

Air  Fountain. — This  consists  of  a  strong  copper  fountain, 
Fig.  148,  with  a  tube,  a  d,  extending  from  the  top  to  the  bottom, 
and  with  a  stop-cock,  c.  To  the  end  of  this  tube  jets  of  any  form 
nay  be  attached.  By  means  of  the  condensing  syringe,  b,  air 

I'ow  sfi  intermittent  springs  accounted  for  ?  Illustrate  the  nature  of  in- 
v  <  litteiH:  springs  by  Tantalus's  cup.  Describe  the  air  fountain.  What 


THE    AIR    FOUNTAIN.  173 

may  be  forced  into  the  fountain  until  it  has 
attained  a  high  degree  of  density.  In  fact, 
a  force  may  be  generated  sufficient  to  burst 
the  vessel  if  it  is  not  very  strong.  It  is  the 
elasticity  of  carbonic  acid  gas  which  some- 
times bursts  soda  fountains,  when  too  large 
quantities  of  this  gas  are  forced  into  them,  and 
condensed  in  the  water  with  which  they  are 
nearly  filled. 

If  we  force  some  air  into  the  fountain,  and 
then  apply  the  revolving  jet,  the  air,  rushing 
out  at  the  sides  of  the  tube  and  removing  the 
pressure,  will  cause  the  jet  to  revolve  with 
great  velocity.  This  action  is  similar  to  that 
of  Barker's  Mill  (page  144). 

The  Air  Gun  is  similar  to  the  fountain,  only  the  bulb  is 
smaller  arid  made  very  strong.  If  the  air  be  compressed  in  it 
about  1600  times  its  volume,  and  then  allowed  to  exert  its  elas- 
ticity upon  the  ball,  it  will  propel  it  with  the  force  of  gunpowder. 
A  ball  is  driven  from  the  ordinary  gun  by  the  elastic  force  of  the 
gases  which  are  formed  by  igniting  the  powder. 

But  the  force  of  compressed  air  in  the  fountain  is  shown  in  a 
more  satisfactory  manner  by  partially  filling  the  fountain  itself 
with  water,  and  then  forcing  into  it  a  quantity  of  air.  The  elas- 
tic force  of  the  air  will  be  exerted  upon  the  surface  of  the  water, 
and  by  means  of  tubes  which  allow  the  water  to  pass  through 
them,  a  beautiful  jet  may  be  formed,  which  will  spout  to  a  great 
height,  and  may  be  made  to  sustain  a  small  ball  placed  upon  its 
summit. 

A  revolving  jet  may  also  be  used.  The  water,  in  this  case, 
will  form  a  disc  of  spray,  as  shown  in  the  figure. 

Sometimes  it  is  desirable  to  make  use  either  of  the  pressure  of 
water  or  of  its  force  through  other  mechanical  media.  In  these 
cases  the  elasticity  of  air  is  often  employed,  by  which  water  is 
raised  to  a  great  height,  and  made  to  flow  in  a  continuous  stream. 
Thus,  in 

What  is  the  principle  of  the  air  gun  ?  What  is  the  force  of  gunpowder 
due  to?  How  are  jets  of  water  produced  by  the  air  fountain? 


174 


NATURAL    PHILOSOPHY. 


Hiero's  Fountain,  by  the  pressure  of  a  column  of  water,  a  jet 
is  thrown  far  above  the  level  of  the  water  in  the  fountain.  The 
fountain  consists  of  two  globes  of  glass,  A  B,  Fig.  Fig.  149. 
149,  connected  by  tubes,  a  b.  One  of  the  tubes, 
a,  passes,  to  the  bottom  of  the  lower  globe,  and  ex- 
tends to  the  top  of  the  plate  or  cup,  D.  A  second 
tube  commences  near  the  top  of  the  ball  A,  and 
extends  into  the  top  of  the  ball  B.  A  third  tube, 
with  a  jet,  passes  into  the  ball  A  and  up  through 
D.  When  the  upper  ball  is  filled  nearly  full  of 
water,  and  a  small  quantity  poured  through  the 
tube  a,  by  which  it  descends  into  the  lower  ball, 
B,  the  air  which  it  contains  will  be  compressed, 
and  the  pressure  will  be  communicated  through 
the  tube  b  upon  the  air  in  A.  This  pressure 
will  be  exerted  upon  the  surface  of  the  water  in 

A,  and  force  it  out  through  the  tube  e  in  the 
form  of  a  jet.     As  the  water  spouts  up  it  falls 
back  into  the  cup  D,  and  runs  down  into  the  ball 

B,  and  by  this  means  a  constant  pressure  is  kept 

up  on  the  surface  of  the  water  in  the  lower  bulb.  The  fountain 
will  continue  to  play,  therefore,  until  all  the  water  is  transferred 
through  the  jet  pipe  from  A  to  B. 

To  the  forcing  ^pump  there  is  usually  attached  a  small  ball 
containing  air  (see  Fig.  145).  As  the  water  is  forced  into  this 
ball,  the  air  is  condensed,  and  by  its  elastic  force  the  stream  is 
kept  constantly  flowing. 

The  Fire  Engine  combines  the  principle  of  the  forcing  pump 
in  connection  with  the  elasticity  of  compressed  air.  There  is  also 
usually  connected  with  it  a  suction  or  lifting  pump,  to  supply  the 
well  of  the  engine  with  water  from  some  cistern  or  reservoir  in 
the  earth. 

Hungarian  Machine. — This  apparatus  was  employed  to  drain 
a  mine  in  Hungary,  and  depends  for  its  action  upon  the  elasticity 
of  air,  the  compression  being  produced  by  a  column  of  water,  as 
in  Hiero's  Fountain. 

Thus  p,  Fig.  150,  represents  a  tube,  into  the  top  of  which 
water  is  made  to  flow  from  a  small  stream.  The  lower  end  of 

Describe  Hiero's  fountain.  •  On  what  principle  does  it  act  ?  Of  what 
use  is  condensed  air  in  the  fire  engine  and  forcing  pump?  Describe  the 
Hungarian  macnine. 


PROBLEMS. 


175 


Fig.  150. 


this  tube  passes  nearly  to  the  bottom  of  an  air-tight  box,/.  Into 
the  under  side  of  the  box  a  tube,  d,  passes 
down  the  side  of  the  pit  into  the  top  of  a 
similar  box,  which  has  a  valve,  a,  in  its 
bottom  to  admit  the  water.  A  third  tube, 
g,  also  extends  to  the  bottom  of  this  box, 
so  as  to  dip  under  the  water,  and  passes 
over  the  sides  of  the  mine,  e.  Now,  when 
the  water  is  let  into  the  tube  p,  it  fills  the 
box  f  partially  full  of  water,  which  con- 
denses the  air  in  the  upper  part  of  it. 
This  condensed  air  transmits  its  force 
through  the  tube  d  to  the  air  in  a,  which 
presses  upon  the  surface  of  the  water,  and 
forces  it  up  through  the  tube  g  to  the  out- 
let of  the  pit.  A  pressure  of  260  feet  of 
water  in  the  pipe  p  raises  the  water  in 
the  mine  to  the  height  of  96  feet,  where 
it  flows  off  by  a  side  drain. 


PROBLEMS. 

1.  A  gas  bag,  half  full  of  air,  was  placed  under  the  receiver  of 
an  air  pump,  and  the  air  exhausted  from  the  receiver  until  the 
expanded  air  filled  the  bag.     What  amount  of  pressure  was  re- 
moved from  «ach  square  inch  of  the  surface  of  the  bag  ? 

Ans.  7*  Ibs. 

2.  An   EBronaut  having  filled  his  balloon  three  quarters  full  of 
gas,  ascended  till  the  gas  expanded  and  filled  the  balloon.     On 
the  supposition  that  his  body  sustained  a  pressure  of  14  tons  at 
the  surface,  what  pressure  would  it  sustain  at  the  height  which 
he  had  then  attained  ?  Ans.  10£  tons. 

3.  A  barometer  at  the  foot  of  a  mountain  stood  at  30  inches  ; 
on  carrying  it  to  the  top,  it  fell  10  inches.     What  was  the  den- 
sity of  the  air  at  its  summit  compared  with  its  density  at  its  foot  ? 

Ans.  fds. 

4.  Into  an  air  fountain  containing  1  cubic  foot  of  space  above 
the  water,  there  was  forced  sufficient  air  to  raise  a  column  of 
water  in  a  tube,  the  section  of  which  was  1  square  inch,  to  the 
height  of  68  feet.     What  was  the  quantity  of  air  forced  into  the 
fountain  ?  Ans.  2  cubic  feet. 


176  NATURAL    PHILOSOPHY. 

5.  To  what  depth  in  the  sea  would  it  be  necessary  to  sink  a 
bag  filled  with  air  in  order  to  compress  it  half  of  its  volume  ? 

Ans.  34  feet. 

6.  A  receiver  containing  1   cubic  foot  of  air  was  exhausted 
till  the  mercury  in  the  gauge  stood  at  20  inches.    What  portion 
of  the  original  quantity  of  air  still  remained  in  the  receiver  ? 

7.  A  barometer  which  stood  at  29-5  inches  at  the  foot  of  a 
mountain,  was  carried  to  its  summit,  where  it  stood  at  27  inches. 
What  was  the  height  of  the  mountain  above  the  valley  ? 

Ans.  2175  feet. 

8.  At  the  foot  of  a  mountain  water  was  found  to  boil  at  a  tem- 
perature of  210  degrees  ;  on  going  to  the  top  it  boiled  at  200°  F. 
What  was  the  height  of  the  mountain  from  its  base,  and  what 
was  the  height  of  the  base  from  the  level  of  the  ocean,  on  the 
supposition  that  the  barometer  stood  at  30  inches  ? 

Ans.  Height  of  mountain,  5500  feet ;  height  of  base  above 
the  ocean,  1100  feet. 

VI.  Diffusion  of  Air  through  other  Matter. — In  consequence 
of  the  great  weight  of  the  air,  its  perfect  fluidity,  and  attraction 
for  other  matter,  it  penetrates  among  the  atoms  of  all  solid,  liq- 
uid, and  gaseous  bodies  whose  pores  permit  it  to  enter.  This  fact 
may  be  proved  and  illustrated  by  numerous  experiments.  Thus, 

1 .  Air  diffuses  itself  among  the  atoms  of  Solids. 

Exp. — Take  any  porous  body,  as  a  piece  of  charcoal,  and  confine  it  at 
the  bottom  of  a  jar  of  water.  Place  the  jar  under  the  exhausted  receiver  of 
the  air  pump,  and  bubbles  of  air  will  be  liberated  from  the  solid  and  pass 
up  through  the  water.  An  egg,  a  piece  of  bone,  a  piece  of  dry  wood,  and 
some  mineral  substances,  will  exhibit  the  same  appearance. 

2.  Air  is  absorbed  by  Liquids,  or  diffuses  itself  among  their 
particles.     This  is  partly  due  to  its  pressure,  and  partly  to  an 
attraction  which  each  has  for  the  other. 

Exp. — Take  a  jar  of  water,  and,  having  placed  it  under  the 
receiver,  exhaust  the  air.  As  the  pressure  is  removed  from  the 
surface  of  the  water,  fine  bubbles  of  air  will  rise  to  the  surface. 

If  a  glass  of  porter,  or  any  other  fermented  liquor,  be  taken, 
Fig.  151,  the  bubbles  of  carbonic  acid  gas  will  be  much  larger, 
and  the  effect  much  more  satisfactory.  It  is  this  acid  which 
is  contained  in  beers,  in  soda  water,  and  in  the  waters  of  cer- 
tain springs,  as  at  Saratoga  (New  York),  and  which  gives  them 
their  pungent  and  pleasant  taste. 

What  experiments  to  show  the  diffusion  of  air  through  solids  and  liquids? 


DIFFUSION    OF    AIR.  177 

It  is  owing  to  the  air  contained  in  water  that  fish  are  able  to 
exist  in  it.  If  they  are  placed  in  a  portion  of  water  from  which 
the  air  is  removed,  they  will  soon  die,  because  the  oxygen  of  the 
air  is  necessary  to  purify  their  blood.  In  performing  the  experi- 
ment upon  fish  under  the  receiver  of  an  air  pump,  they  will  rise 
to  the  surface  after  a  few  strokes  of  the  piston,  owing  to  the  ex- 
pansion of  the  air  in  the  air  bladder  within  them,  and,  by  con- 
tinuing to  exhaust  the  air,  the  bladder  will  burst,  and  they  will 
sink  to  the  bottom  of  the  vessel. 

3.  Air  diffuses  itself  through  other  Gases.  The  power  of 
gases  to  diffuse  themselves  through  each  other  is  quite  remark- 
able. The  fact  may  be  shown  experimentally,  with  regard  to 
any  two  gases,  by  confining  them  in  jars,  and  allowing  them  to 
communicate  with  each  other. 

Fig.  152.  Thus,  if  we  take  a  jar  of  hydrogen  gas,  H,  Fig. 
152,  which  is  several  times  lighter  than  air,  and  invert 
it  over  a  jar  of  air,  C,  the  hydrogen  will  descend  into  the 
lower  jar,  and  the  air,  at  the  same  time,  rise  into  the 
upper  jar.  In  a  short  time  they  will  be  mingled,  as 
may  be  proved  by  transferring  the  gases  from  each  jar 
separately  into  a  hydrogen  pistol  and  explo<^g  them. 
The  same  diffusion  takes  place  when  a  jar  of  air  ia 
placed  over  one  of  carbonic  acid,  though  the  air  is  much 
lighter  than  the  acid. 

The  law  which  governs  them,  as  they  mingle  with  each  oth- 
er, has  been  ascertained  by  experiment,  and  it  is  found  that 

The  velocities  with  which  Gases  flow  into  each  oilier  are  in- 
versely as  the  square  roots  of  their  densities.  Hence  the  veloci- 
ty of  the  lighter  gas  is  much  greater  than  that  of  the  heavier 
gas.  Thus,  if  air  were  sixteen  times  as  dense  as  hydrogen,  it 
would  flow  with  but  one  quarter  of  the  velocity.  This  tenden- 
cy to  diffusion  is  manifested  most  strikingly  when  there  is  a  por- 
ous partition,  as  a  stopper  of  plaster  of  Paris,  between  the  two 
gases.  Gases  will  also  mingle  through  substances  which  are 
not  considered  porous.  Hydrogen  gas  in  a  soap  bubble  will  pass 
out,  and  air  will  pass  in. 

How  are  fish  enabled  to  exist  in  water  ?  What  is  the  law  when  gases 
mingle  with  each  other?  Which  has  the  greater  velocity  ? 

H2 


178  NATURAL    PHILOSOPHY. 


VII.  Buoyancy  of  the  Air.-^WQ  have  seen  that  water  will 
float  bodies  specifically  lighter  than  itself. 
The  same  is  true  of  the  air.  This  is  due  to 
its  weight  or  pressure.  Hence  a  balloon,  Fig. 
153,  filled  with  hydrogen  gas  or  with  heated 
air,  will  be  carried  up  into  the  atmosphere  in 
the  same  manner  that  a  cork  when  placed  un- 
der water  will  rise  to  its  surface.  The  heav- 
ier air  surrounding  the  balloon  lifts  it  up  by  its 
superior  pressure  ;  hence,  if  the  surface  of  a 
body  is  increased,  while  its  quantity  of  matter  remains  the  same, 
it  will  be  buoyed  up.  If,  therefore,  a  body  be  weighed  in  air,  it 
will  weigh  less  than  if  weighed  in  hydrogen  gas  or  in  a  vacuum, 
just  as  a  body  will  weigh  less  in  water  than  in  air.  Now,  as  the 
power  of  any  fluid  to  sustain  bodies  in  it  depends  upon  the  sur- 
face exposed,  the  quantity  of  matter  being  the  same,  it  will  be 
easy  to  see  that  the  same  quantity  of  matter  in  its  most  concen- 
trated form,  that  of  a  sphere,  would  weigh  in  air  more  than  when 
made  into  a  large  hollow  balloon.  Hence  it  is  true 
that  a  'J^ound  of  feathers  is  heavier  than  a  pound  of 
lead  ;"  that  is,  contains  a  larger  quantity  of  matter. 

Exp.  —  This  principle  may  be  illustrated  by  a  thin  glass 
globe,  Fig.  154,  balanced  by  a  metal  weight  in  air.  When 
placed  under  the  receiver,  and  the  air  exhausted,  the  glass 
will  be  seen  to  be  the  heavier.  It  is  owing  to  the  buoyancy 
of  the  air  that  smoke  and  clouds  are  borne  up  by  it. 

VIII.  Resistance  of  the  Air.  —  Air,  as  well  as  water,  opposes 
a  resistance  to  bodies  passing  through  it.  The  force  of  resistance 
is  as  the  square  of  the  velocity.  Hence,  in  rapid  motions,  as  that 
of  a  cannon  ball,  this  force  becomes  very  great.  It  has  been 
found  difficult  to  give  a  cannon  ball  a  velocity  of  2000  feet  per 
second.  When  the  velocity  is  more  than  about  1280  feet  per  sec- 
ond, the  resistance  is  suddenly  augmented.  This  is  due  to  the  fact 
that  the  velocity  of  air  flowing  into  a  vacuum  is  about  1280  feet 
per  second,  and  above  this  velocity  the  pressure  is  removed  from 
the  back  of  the  ball,  the  air  not  flowing  in  to  equalize  the  pressure. 

What  example  of  the  buoyancy  of  the  air  ?  What  is  the  law  of  resist- 
ance to  bodies  passing  through  the  air? 


RESISTANCE'  OP    THE    AIR. 


179 


It  is  owing  to  the  resistance  of  the  air  that  bodies  falling  through 
Fig.  155.      it  are  retarded  in  proportion  as  their  surfaces  are 
enlarged.     Were  it  not  for  this  resistance,  all  bodies 
would  fall  from  the  same  height  in  the  same  time, 
whatever  their  size  or  weight. 

Exp. — To  illustrate  this  principle,  take  a  guinea  and  feath- 
er, or  piece  of  paper,  and  suspend  them  in  a  long  glass  tube, 
Fig.  155.  By  allowing  these  to  fall  in  the  tube  filled  with 
air,  it  will  be  seen  that  the  guinea  falls  with  a  much  greater 
velocity  than  the  feather.  On  exhausting  the  air,  they  will 
fall  in  the  same  time. 

It  is  owing  to  the  resistance  of  the  air  that  wind- 
mills, fans,  and  fan-mills  are  made  to  revolve.  As 
the  force  of  resistance  depends  upon  the  extent  of 
surface  exposed,  their  power  may  be  increased  with 
an  increase  of  surface ;  and  by  so  arranging  the 
wheels  and  floats  that  the  rotary  motion  shall  cause  the  fans  to 
cut  the  air,  while  the  propelling  force  of  the  wind  strikes  upon 
the  broad  surface  of  the  fan,  a  large  proportion  of  the  force  of  the 
wind  is  made  effective  to  turn  the  mill. 

To  illustrate  this  difference,  take  two  thin  fans,  fastened  to  an 
axis  having  two  centers,  so  that  it  may  revolve  either  flatwise  or 
edgewise,  and  present  first  the  broad  surface  and  then  the  edges 
to  the  air,  and  turn  them  rapidly  with  the 
finger.  In  the  former  case  they  will  soon 
stop,  in  the  latter  they  will  continue  to  re- 
volve for  some  time. 

Or  two  fan- wheels,  Fig.  156,  may  be 
made  to  revolve  first  in  a  vacuum  and  then 
in  the  air ;  one,  b,  with  its  broad  surfaces  ex- 
posed to  the  air  in  each  case,  and  the  other, 
a,  with  its  edges,  and  their  speed  will  be 
found  to  differ  greatly  in  the  air,  but  to  be 
exactly  equal  in  the  vacuum. 

The  sky-rocket,  and  many  articles  used 
in  pyrotechny,  depend  upon  the  resistance  of  the  air.  As  this 
resistance  increases  with  the  square  of  the  velocity,  it  is  found  by 

What  principle  do  the  guinea  and  feather  illustrate?  How  may  the 
force  of  wind-wheels  be  increased  ?  Illustrate.  Upon  what  force  does  the 
ascent  of  the  sky-rocket  depend  ? 


Fig.  156. 


180 


NATURAL    PHILOSOPHY. 


experiment  that  a  train  of  cars  running  at  the  rate  of  fifty  or 
sixty  miles  per  hour,  requires  a  very  great  addition  of  force  to 
overcome  the  resistance  of  the  air.  Especially  is  this  the  case  if 
the  air  is  moving  in  the  opposite  direction. 

IX.  Motion  of  the  Air  and  other  Gases. — When  air  or  any 
other  gas  is  placed  in  any  vessel,  as  in  the  air  fountain,  and  an 
aperture  made,  it  will  flow  out,  provided  its  density  is  greater 
than  the  surrounding  air.  The  laws  by  which  its  motion  is  reg- 
ulated through  thin  walls  and  through  tubes  are  very  similar  to 
those  which  pertain  to  the  efflux  of  liquids,  which  we  have  al- 
ready considered.  When  air  is  condensed  in  the  air  fountain  and 
allowed  to  escape,  its  velocity  decreases  in  a  similar  manner  to 
that  of  a  liquid  spouting  from  an  orifice  near  the  bottom  of  a  ves- 
sel filled  with  water,  and  allowed  to  empty  itself.  But  if  the 
compressing  force  is  a  column  of  water,  which  is  kept  constantly 
at  the  same  height,  as  is  the  case  in  the  gasometer,  then  the 
velocity  of  the  efflux  is  constant,  and  is  similar  to  that  of  a  liquid 
spouting  from  a  vessel  kept  constantly  full  of  water. 

The  Gasometer,  Fig.  157,  is 
simply  a  cylindrical  vessel,  G, 
open  at  the  bottom,  and  sunk  in 
a  well,  w,  or  similar  cylinder 
open  at  the  top,  and  filled  with 
water.  The  gas  is  conducted 
through  the  water,  and  lifts  the 
gasometer  as  it  fills.  A  force  r 
then  may  be  applied,  by  means 
of  weights,  which  shall  cause 
the  water  to  rise  higher  on  the 
outside  than  on  the  inside  of  the 
gasometer,  and,  of  course,  as  the  gas  flows  out  through  an  open- 
«.*£,,  c,  the  weights  cause  the  gasometer  to  sink,  so  that  the  height 
of  the  water  is  the  same  until  the  whole  is  discharged.  The 
amount  of  condensation  will  depend  upon  the  height  of  the  water 
column,  which  may  be  increased  or  diminished  by  adding  larger 
or  smaller  weights  to  the  gasometer.  A  gauge,  h  i,  is  sometimes 
applied  to  pipes  conducting  air,  for  the  purpose  of  ascertaining 

What  conditions  are  necessary  to  the  motion  of  gases?  What  laws  regu- 
late the  efflux  of  gases  ?  Describe  the  gasometer.  What  is  the  use  of  tha 
gauge  ? 


Fig.  157. 


MOTION    OF    GASES.  181 

the  amount  of  pressure.  The  difference  between  the  height  of 
the  column  of  water  in  the  two  arms  of  the  gauge  will  indicate 
the  amount  of  pressure. 

The  velocity  of  gases  and  the  quantity  of  efflux  are  determin- 
ed in  the  same  way  as  in  the  case  of  liquids,  but  the  degree  of 
elasticity,  which  is  the  impelling  force,  is  represented  by  a  col- 
umn of  water,  since  air  is  not  of  equal  density.  A  column  of 
water  34  feet  high  will  reduce  the  volume  of  a  confined  portion  of 
air  one  half,  or  will  double  its  density.  Now  the  velocity*  of  air 
thus  condensed  will  be  equal  to  that  which  a  falling  body  would 
acquire  in  falling  through  a  perpendicular  height  represented  by 
the  column  of  water.  Water  is  about  770  times  the  density  of 
air,  so  that  the  height  in  this  instance  would  be  770  times  34 
feet,  or  26,180  feet ;  and  the  velocity  acquired  by  a  body  falling 
through  this  space  would  be  about  1294  feet  per  second  (see  page 
66).  Now  the  pressure  of  the  air  at  the  surface  in  reference  to 
a  vacuum  is  precisely  similar  to  the  condensed  air  in  the  above 
example  in  relation  to  air  at  the  common  density,  and  hence  air 
would  flow  into  a  vacuum  about  1294  feet  per  second.  The  ve- 
locity is  generally  estimated,  however,  at  1280  feet,  as  air  at  its 
medium  pressure  will  not  sustain  a  column  of  water  quite  34  feet 
in  height,  and,  of  course,  the  height  of  the  air  column  would  be 
less  than  in  the  above  estimate.  The  velocity  and  quantity  are 
influenced,  also,  by  the  orifice,  as  in  the  case,  of  liquids,  so  that 
the  actual  quantity  discharged  in  a  given  time  will  be  somewhat 
less  than  the  theory  requires. 

The  lateral  pressure  of  gases,  as  air,  in  conducting  pipes,  is 
similar  to  that  of  water.  Long  tubes,  in  consequence  of  friction, 
diminish  the  velocity  and  quantity  of  efflux.  The  resistance  pro- 
duced by  the  friction  is  proportioned  to  the  length  of  the  tube ; 
but  the  larger  the  tube,  the  less  the  resistance,  or  the  resistance 

*  Let  £=the  intensity  of  the  force  of  gravity  in  the  latitude  of  New 
York  for  one  second  =16TV  feet.  Then  we  shall  have  the  formula  v=. 
SiVgh;  h  representing  the  height  of  the  air  column,  which,  of  course,  will 
vary  with  the  degree  of  density  of  the  compressed  air. 

How  is  the  velocity  of  air  flowing  into  a  vacuum  determined  ?  What  in- 
ftuence  have  conducting  pipes  upon  the  velocity  of  gases  flowing  through 
them? 


182  NATURAL    PHILOSOPHY. 

is  inversely  as  the  diameter  of  the  tube,  and  increases  as  the 
square  of  the  velocity  of  the  flowing  gas.  There  is  also  a  "  con- 
tracted vein,"  as  in  the  case  of  liquids,  though  it  can  not  be  di 
rectly  observed,  and  hence  short  tubes  increase  the  quantity  of 
efflux. 

When  air  is  condensed  and  flows  through  an  aperture  in  the 
side  of  a  vessel,  or  through  a  tube  which  is  terminated  by  a  flat 
disc,  there  is  produced  the  phenomenon  of  suction;  that  is,  a 
partial  vacuum  is  formed  near  the  sides  of  the  opening. 

Thus,  if  a  tube,  p,  Fig.  158,  with  a  disc,  b  c, 
be  inserted  in  the  air  fountain,  and  a  card  or 
piece  of  metal,  a,  two  thirds  the  diameter  of  the 
disc,  placed  upon  it,  directly  over  the  aperture, 
the  card  can  not  be  blown  off  by  the  force  of  the 
condensed  air,  but,  after  the  first  impulse,  will 
vibrate  at  a  very  short  distance  from  the  aper- 
ture, while  the  air  will  rush  out  between  it  and  the  disc  with 
considerable  noise.  A  pin  should  be  forced  through  the  center 
of  the  card,  extending  into  the  aperture,  to  keep  the  card  in  its 
place. 

This  singular  fact  is  thus  explained  :  As  the  air  moves  with 
greater  velocity  at  the  center  than  at  the  sides  of  the  tube,  the 
moment  of  its  escape  through  the  top  of  the  disc,  its  lateral  press- 
ure causes  it  to  be  spread  in  a  thin  layer  between  the  disc  and 
the  card,  by  which  a  partial  vacuum  is  formed  around  the  side 
and  over  the  disc,  as  represented  in  Fig.  158,  and  the  external 
pressure  of  the  air  confines  the  card  firmly  to  the  disc.  This 
principle  is  no  doubt  the  cause  of  the  effect  produced  by  certain 
fixtures  for  the  purposes  of  ventilation. 

SECTION  II.— THE  ATMOSPHERE.    METEOROLOGY. 

The  atmosphere  is  that  gaseous  fluid  which,  surrounds,  the 
earth.  The  description  and  explanation  of  its  phenomena  con- 
stitute the  science  of  Meteorology. 

I.  The  iveight  of  the  atmosphere  is  determined  by  means  of 
the  barometer,  and  is  sufficient  to  counterbalance  an  ocean  of 
mercury  encircling  tJib  earth  2-5  feet  in  depth,  and  a  similar 
ocean  of  water  34  feet  in  depth. 

How  is  the  phenomenon  of  suction  explained  ? 


WEIGHT    OF    THE    ATMOSPHERE.  183 

II.  The  density  of  the  atmosphere  diminishes  as  we  ascend 
from  the  surface  of  the  earth  in  a  geometrical  ratio,  as  the 
height  increases  in  an  arithmetical  ratio. . 

III.  The  Jieight  of  the  atmosphere  is  about  50  miles.     This 
is  determined  by  the  limit  which  is  put  to  its  elasticity  by  the 
weight  of  its  particles  at  that  height,  and  also  by  the  phenomena, 
of  the  refraction  of  light. 

IV.  The  temperature  of  the  atmosphere  diminishes  from  the 
equator  toivard  the  poles  ;  and,  as  we  ascend  above  the  surface 
of  the  earth,  the  thermometer  sinks  about  one  degree  for  every 
352feet. 

V.  The  motions  of  the  atmosphere,  or  the  phenomena  of  winds, 
are  occasioned  by  the  unequal  distribution  of  heat.     Winds  are 
variously  named,  as  trade  winds,  land  and  sea  breezes,  hurri- 
canes, tornadoes,  fyc. 

VI.  The  moisture  of  the  atmosphere  varies  at  different  places, 
and  at  the  same  place  at  different  times.    The  quantity  of  moist- 
ure is  ascertained  by  means  of  the  hygrometer.     Its  condensa- 
tion gives  rise  to  dews,  frosts,  clouds,  rain,  snow,  and  hail. 

VII.  Meteorolites  and  electrical  phenomena  may  also  be  in- 
cluded in  a  description  of  the  atmosphere.     Also 

VIII.  Its  relations  to  animals,  and  to  the  principles  of 

IX.  'Ventilation,  or  the  laivs  ivhich  pertain  to  the  draughts 
of  chimneys,  and  the  processes  by  which  foul  air  is  withdrawn 
from  the  apartments  of  buildings  and  pure  air  introduced. 

HAVING  considered  the  properties  of  air,  we  are  now  prepared 
to  study  the  phenomena  of  the  atmosphere,  its  weight,  density, 
height,  relations  to  heat,  moisture,  winds  and  dews,  electrical 
changes,  &c.  The  description  and  explanation  of  the  phenom- 
ena of  the  atmosphere  constitute  the  science  of  Meteorology. 

I.  Weight  of  the  Atmosphere. — The  weight  of  a  column  of  air 
of  one  square  inch  in  surface,  extending  to  the  top  of  the  atmo- 
sphere, is  sufficient,  as  we  have  seen,  to  sustain  a  column  of  mer- 
cury two  feet  and  five  tenths  in  height,  and  a  column  of  water 
thirty-four  feet  in  height.  This  mercury  weighs  fifteen  pounds, 

How  is  the  weight  of  the  atmosphere  determined  ? 


184  NATURAL   PHILOSOPHY. 

or,  more  exactly,  fourteen  and  seven  tenths.  Knowing  the  weight 
of  air  pressing  upon  one  square  inch  of  surface,  it  is  easy  to  cal- 
culate the  weight  of  the  whole  atmosphere ;  for  if  we  can  de- 
termine the  number  of  square  inches  contained  in  the  whole 
earth's  surface,  and  then  multiply  these  by  fifteen,  it  will  give 
us  the  absolute  weight  of  the  whole  atmosphere.  The  number 
of  square  inches  on  the  surface  of  our  globe  is  found  by  multiply- 
ing the  circumference  by  the  diameter,  or  four  times  the  square 
of  the  radius  of  the  earth  by  3*1416.  The  weight  thus  calcu- 
lated is  found  to  be  more  than  eleven  trillions  of  pounds,  or  five 
thousand  billions  of  tons.  This  weight  would  be  sufficient  to 
counterbalance  an  ocean  of  mercury  encircling  the  earth  2' 5 
feet  in  depth,  or  an  ocean  of  water  34  feet  deep. 

II.  Density  of  the  Atmosphere. — The  density  of  the  atmos 
phere  at  the  earth's  surface  is  determined  by  the  weight  of  a 
given  quantity  at  the  standard  temperature  and  pressure,  com- 
pared with  an  equal  weight  of  water  ;  for,  as  atmospheric  air  is 
taken  as  a  standard  by  which  to  compare  other  gases  and  vapors, 
its  density  must  be  determined  by  that  of  some  other  body  of 
known  density,  as  water  or  mercury.  Air  is  found  to  be  about 
TTi_^ths  as  dense  as  mercury,  and  T¥y¥oths  as  dense  as  water. 
It  is  not  constant  in  its  density ;  at  a  medium  pressure  its  density 
is  Tj-i^th,  the  specific  gravity  of  water  being  1,  that  of  mercury  13- 6. 

The  density  of  the  air  is  not  equal  throughout  its  whole  ex- 
tent ;  for,  as  the  air  is  an  elastic  fluid,  the  lower  strata  are  pressed 
upon  by  those  above  them,  and,  as  we  rise  above  the  level  of  the 
sea,  the  density  of  the  atmosphere  diminishes  in  a  definite  ratio  ; 
for,  according  to  the  law  of  Mariotte, 

The  volume  of  the  air  is  inversely  as  the  compressing  force ; 
and,  as  we  ascend,  the  compressing  force  constantly  diminishes. 

This  decrease  of  pressure  is  indicated  by  the  barometer.  It  is 
found  by  observation,  aided  by  calculation,  that  at  the  height  of 
seven  miles  it  is  but  a  quarter  as  dense  as  at  the  surface  of  the 
earth.  Now,  as  this  distance  is  doubled,  the  density  is  one  quar- 

To  what  is  it  equal  ?  What  is  life  density  of  air  at  the  surface  of  the 
earth  1  Does  it  decrease  in  density  ?  According  to  what  law  1  Illustrate 
the  law  of  Mariotte. 


DENSITY    OF    THE    ATMOSPHERE. 


185 


ter  as  great,  or  TVt^  at  three  times  the  distance,  ?'Tth  as  great. 
Hence,  if  we  take  the  series  7,  14,  21,  &c.,  we  shall  find  that 
the  density  will  "be  £,  TV,  Q\,  &c. ;  or,  if  the  heights  form  an 
arithmetical  series,  the  densities  diminish  in  a  geometrical  ratio.* 

At  the  height  of  twenty-one  miles,  therefore,  the  atmosphere 
is  sixty-four  times  rarer  than  at  the  surface  of  the  earth,  and  at 
the  height  of  one  hundred  miles  one  thousand  million  times  rarer. 

On  the  other  hand,  if  the  atmosphere  were  allowed  to  enter 
the  earth  through  an  aperture  in  the  direction  of  its  center,  its 
density  would  increase  by  the  same  law.  At  the  depth  of  seven 
miles,  it  would  be  four  times  as  dense  as  at  the  surface  ; '  at  four- 
teen miles,  sixteen  times  as  dense,  giving  the  series 

7,    14,    21,     28,       35,        42,         49,          56, 
4,    16,    64,    256,    1024,    4096,    16384,    65536. 
The  air  would  be  denser  than  water  at  thirty-five  miles,  densei 
than  mercury  at  forty-nine  miles,  and  denser  than  platinum  or 
any  known  body  at  fifty-six  miles. — Olmsted. 

If  there  were  no  disturbing  causes,  the  exact  density  of  the  air 
at  different  heights  might  be  accurately  defined.  But  there  are 
several  facts  not  yet  noticed  which  must  be  taken  into  account. 
The  upper  portions  of  the  atmosphere  are  further  from  the  earth's 
center ;  and,  therefore,  as  the  force  of  gravity  diminishes  as  the 
square  of  the  distance,  particles  of  air  in  the  upper  strata  weigh 
less  than  those  in  the  lower.  The  attraction  of  the  sun  and  moon 

*  The  following  table  by  Mr.  Lubbock  shows  the  constitution  of  the  at- 
mosphere according  to  the  most  accurate  observations  hitherto  made : 


Height  in 
Miles. 

Pressure. 

Temperature. 

Density. 

0 
1 

Inches. 

30-00 
24-61 

Fahr. 

4-50-0 
35-0 

1,00000 
,84611 

2 

20-07 

19-5 

,71294 

3 
4 
5 
10 

16-25 
13-06 
10-41 
2-81 

+3-4 
—13-3 
—30-6 
—126-4 

,59798 
,49903 
,41403 
,14499 

15 

•45 

—240-6 

,03573 

What  would  be  the  law  of  increase  of  density  if  the  air  extended  toward 
the  center  of  the  earth  ?  What  causes  interfere  with  the  law  of  the  de- 
crease of  density  ?  . 


186  NATURAL   PHILOSOPHY. 

is  also  greater  the  nearer  the  atoms  are  to  diem,  which  will  tend 
to  render  them  lighter. 

In  the  upper  regions  of  the  atmosphere,  too,  heat  and  cold,  and 
the  formation  of  clouds  interfere,  in  some  degree,  with  the  law. 
As  heat  expands,  and  cold  contracts,  and  moisture  diminishes  its 
weight,  in  determining  the  exact  density  of  the  atmosphere,  all 
these  circumstances,  except  perhaps  attraction,  which  is  exceed- 
ingly small  at  ordinary  heights,  must  be  considered. 

III.  Height  of  the  Atmosphere.*— If  the  air  were  of  uniform 
density  we  could  easily  determine  its  height,  since  the  heights  of 
any  two  fluids  are  inversely  as  their  specific  gravities.  Since, 
then,  the  specific  gravity  of  air  is  to  mercury  as  1  to  11500,  its 
height  would  be  obtained  by  this  proportion — 1  :  11500  :  :  height 
of  a  column  of  mercury  30  inches  :  height  of  the  atmosphere ;  or, 
1  :  11500  :  :  2'5  ft.  :  28750 =5£  miles.  On  the  other  hand,  if 
we  apply  the  law, 

That  the  density  diminishes  in  a  geometrical  ratio  as  the  height 
increases  by  an  arithmetical  ratio,  it  is  evident  that  the  atmos- 
phere would  be  unlimited  in  extent,  reaching  to  the  most  distant 
regions  of  space.  But  there  are  several  reasons  for  believing 
that  the  atmosphere  is  limited,  and  that  we  may  determine  its 
height  very  nearly. 

1 .  The  elasticity  of  the  air  is  produced  by  a  mutual  repulsion 
between  its  particles  ;  but  this  repulsion  is  overcome  in  the  high- 
er regions  of  the  atmosphere  by  two  causes,  the  increase  of  cold, 
and  the  attraction  of  gravitation ;  for  the  force  of  gravitation  de- 
creases but  little  at  the  height  of  fifty  miles,  while  the  elastic 
force  is  greatly  decreased.     At  about  this  height  the  weight  of 
the  particles  will  overcome  their  repulsion,  and  thus  prevent  the 
further  extension  of  the  atmosphere. 

2.  This  view  is  confirmed  by  reference  to  the  phenomena  of 
refraction.     Light  is  not  refracted  higher  than  sixty  miles,  which 
shows  that  the  space  above  is  destitute  of  air. 

What  effect  have  heat,  cold,  and  moisture  on  the  density  of  the  atmos- 
phere ?  How  could  the  height  of  the  atmosphere  be  determined  if  the  air 
were  of  uniform  density,  and  what  would  be  its  extent  ?  How  far  would 
the  atmosphere  extend  by  Mariotte's  law  ?  What  reason  for  believing  that 
the  atmosphere  is  limited  in  extent  ? 


TEMPERATURE  OF  THE  ATMOSPHERE.         187 

IV.  Temperature  of  the  Atmosphere. — The  temperature  of  the 
atmosphere  on  the  surface  of  the  earth  is  very  various.  It  gen- 
erally diminishes  fi^n  the  equator  toward  the  poles,  but  not 
equally.  There  are  many  disturbing  causes  which  tend  to  in- 
crease the  mean  annual  temperature*  in  the  same  parallel  of 
latitude.  Some  of  these  disturbing  causes  are  the  situation  of  the 
land  in  reference  to  water,  or  to  currents  in  the  ocean ;  the  vicin- 
ity of  deserts  or  high  mountains,  and  the  direction  of  the  wind, 
also  exert  more  or  less  influence  upon  the  temperature.  These 
variations  are  frequently  represented  on  a  chart  thus  : 

Through  those  places  where  the  mean  height  of  the  thermom- 
eter is  the  same  during  the  summer,  lines  are  drawn  called  isoth- 
eral  lines;  and  through  those  places  in  which  the  mean  tem- 
perature during  the  winter  is  the  same,  similar  lines  are  drawn, 
called  isochimenal  lines.  These  lines,  owing  to  the  various  causes 
above  alluded  to,  are  somewhat  irregular  in  their  course  around 
the  earth,  and  places  which  have  the  same  mean  annual  temper- 
ature often  differ  in  the  extremes  of  heat  and  cold  during  the 
year.  Lines  passing  through  such  places  are  called  isothermal. 

The  temperature  of  the  atmosphere  as  we  ascend  above  the 
level  of  the  sea  is  constantly  diminishing,  until  we  arrive  at  a 
point,  varying  in  different  latitudes,  where  water  is  congealed. 
Under  the  equator  we  reach  this  point  at  about  the  height  of 
three  miles.  At  the  poles  it  is  at  the  surface  of  the  earth.  The 
lower  limit  of  this  region  is  called  ihe*curve  of  perpetual  conge- 
lation. Hence  mountains  which  rise  above  this  limit  are  cover- 
ed with  perpetual  snow  and  ice.  By  numerous  observations  and 
calculations  which  have,  been  derived  from  the  mean  temperature 
and  known  decrease  of  heat  at  different  heights,  the  line  of  per- 
petual congelation  has  been  determined  for  every  parallel  of  lati- 
tude from  the  equator  to  the  poles. 

*  By  mean  annual  temperature  is  meant  the  mean  height  of  the  thermom- 
eter during  the  year.  Thus  we  might  ascertain  the  mean  temperature  for 
a  single  day  by  noting  the  height  of  the  mercury  for  each  hour,  and  then 
dividing  this  by  24.  The  mean  annual  temperature  is  sometimes  ascertained 
approximately  by  the  temperature  of  water  in  a  deep  well,  which  is  nearly 
uniform  during  the  whole  year. 

Is  the  atmosphere  of  the  same  temperature  throughout  ?  What  is  meant 
by  the  curve  of  perpetual  congelation,  and  what  is  the  form  of  this  curve  ? 


188  NATURAL    PHILOSOPHY. 


Thus,  at  the  equator, 

Deg.  Ht.  in  ft. 

0° 15577 

10° 15067 

20° ..13719 

30°..  ..11592 


Deg.  Ht.  in  ft. 

40° ^ 9016 

50° m 6260 

60° 3684 

80°..  .  120 


This  line,  it  will  be  seen,  approaches  near  the  earth  in  a  more 
rapid  ratio  as  we  approach  the  poles,  though  the  greatest  differ- 
ence is  between  forty  and  fifty  degrees.  The  reason  for  the  cold 
in  the  higher  regions  of  the  atmosphere  is  found  in  two  well-known 
laws. 

1.  The  air  is  not  heated  by  the  sun's  rays  passing  directly 
through  it,  but  by  contact  with  the  heated  earth. 

2.  As  each  portion  becomes  heated,  it  rises  up,  but  not  to  the 
top  of  the  atmosphere.     As  it  rises  ft  expands,  and  its  capacity 
for  heat  increases  and  diminishes  its  temperature,  so  that  it  will 
soon  arrive  at  a  region  where  the  air  is  of  equal  density,  and  there 
remain.     By  the  heat  of  the  sun,  then,  the  atmosphere  is  heated 
only  to  a  limited  extent.     Above  this  limit,  as  the  pressure  is  less, 
its  expansion  is  greater,  and  its  capacity  for  heat  increases.    Hence 
the  air  must  be  colder  the  higher  we  ascend.     This  fact  has  also 
been  confirmed  by  aeronauts,  who  experience  the  sensation  of  cold 
in  proportion  to  their  height  above  the  surface. 

V.  Phenomena  of  Winds. — Winds  are  created  by  any  disturb- 
ance of  the  equilibrium  of  the  atmosphere.  The  principal  agent 
in  producing  this  disturbance  is  the  heat  of  the  sun,  which  acts 
unequally  in  different  latitudes  arid  on  different  surfaces  in  the 
same  latitude.  The  principle  upon  which  winds  are  produced 
may  be  illustrated  by  reference  to  very  common  phenomena. 

By  holding  a  lighted  taper  in  the  crevice  of  a  door  when  there 
is  a  fire  in  the  room,  it  will  be  observed  that  there  is  a  current 
of  air  inward  at  the  bottom  and  outward  at  the  top. 

The  draft  of  a  chimney  also  illustrates  the  same  fact.  When 
a  fire  is  made,  the  heated  air  rises,  the  colder  air  of  the  room  flows 
toward  the  fire,  and  the  smoke  is  carried  up  by  the  current  of  air 
thus  produced.  When  the  air  in  the  room  is  warmer  than  that 

What  is  the  cause  of  the  cold  in  the  higher  regions  of  the  atmosphere  1 
How  are  winds  produced  1  Illustrate  the  manner  in  which  air  is  made  to 
circulate  in  chimneys,  &c. 


WINDS TRADE  WINDS.  189 

in  the  chimney,  there  is  a  downward  current.  On  this  principle, 
mines  are  sometimes  kept  cool  and  purified  of  foul  air  by  two 
shafts,  one  longer  than  the  other,  situated  at  either  extremity  of 
the  mine.  The  air  in  summer  will  moVe  down  the  longer  shaft 
and  outward  at  the  shorter  one.  In  winter  the  external  air  is 
cooler  than  that  in  the  mine,  and  it  flows  down  the  shorter  and 
out  at  the  longer  shaft.  In  the  spring  and  fall  the  air  is  station- 
ary, and  then  the  miners  complain  of  bad  air.  It  requires  but  a 
slight  difference  of  temperature  to  produce  a  draft ;  thus,  if  we 
take  a  syphon  tube,  and  put  a  piece  of  ice  into  the  long  arm,  cur- 
rents of  air  will  circulate  through  the  longer  and  out  at  the  shorter 
arm  of  the  tube. 

The  equatorial  regions  receive  the  direct  rays  of  the  sun ;  and 
the  atmosphere,  being  more  heated  in  those  regions,  expands  and 
rises  up,  while  the  colder  air  from  either  pole  flows  toward  the 
equator  to  supply  its  place.  Hence  we  should  suppose  that  the 
winds  would  follow  the  apparent  course  of  the  sun.  Such  is 
found  to  be  the  fact.  As  such  winds  flow  in  definite  directions, 
navigators  take  advantage  of  them  in  crossing  the  ocean,  and 
hence  they  are  called 

1.  Trade  Winds.  —  The  trade  winds  on  the  north  of  the 
equator  are  from  the  northeast,  and  on  the  south  side  from  the 
southeast,  extending  over  a  belt  of  the  earth  of  about  sixty  de- 
grees, thirty  on  each  side  of  the  equator. 

The  reason  that  these  currents  do  not  move  directly  toward 
the  equator,  the  place  of  greatest  rarefaction,  is,  that  the  atmos- 
phere moves  with  the  earth  from  west  to  east,  but  the  velocity 
is  less  the  further  we  go  from  the  equator.  A  current  starting 
at  sixty  degrees  north  of  the  equator,  and  flowing  directly  south, 
passes  over  portions  of  the  earth  whose  velocity  is  constantly  in- 
creasing, and  hence  the  wind,  moving  toward  the  east  with  less 
velocity  than  the  portions  of  the  earth  over  which  it  is  flowing, 
appears  to  move  from  the  northeast  to  the  southwest ;  and,  owing 
to  the  fact  that  the  earth  is  moving  toward  the  east  faster  than 
the  wind  is,  the  latter  is  in  the  condition  of  a  body  acted  upon 

How  are  the  trade  winds  produced  ?  What  is  the  direction  of  the  trade 
winds  ?  What  causes  appear  to  alter  their  course  ? 


190  NATURAL    PHILOSOPHY. 

by  two  forces,  and  it  describes  the  diagonal  of  a  parallelogram,  or 
moves  in  a  southwest  direction  ;  for  a  similar  reason,  the  currents 
which  flow  from  the  south  are  deflected,  and  flow  in  a  northwest 
direction  toward  the  equator. 

When  the  northeast  trade  wind  meets  the  southeast  trade  wind, 
they  unite  and  flow  toward  the  west ;  but,  in  consequence  of  the 
velocity  with  which  the  heated  air  rises  up,  their  westerly  motion 
is  almost  perfectly  neutralized,  and  hence  there  is  formed  a  zone 
called  the  region  of  calm?,.  The  center  of  this  zone  lies  a  little 
north  of  the  equator,  and  varies  at  different  seasons  of  the  year. 

The  air  which  rises  up  at  the  equator  flows  toward  the  poles, 
forming  upper  trade  winds,,  which  flow  in  an  opposite  direction 
to  those  below,  and  as  they  descend  toward  the  earth,  constitute 
southwest  winds  in  the  northern,  and  northwest  in  the  southern 
hemisphere.  North  of  the  equator,  northeast  and  southwest 
winds  prevail  until  we  reach  high  latitudes,  where  they  seem  to 
change  their  direction.  The  existence  of  these  winds  has  been 
ascertained  by  the  direction  given  to  the  ashes  in  volcanic  erup- 
tions when  they  have  risen  to  a  great  height,  and  by  the  direction 
of  the  wind  on  the  summits  of  high  mountains  in  the  region  of 
the  trade  winds.  Thus,  at  the  summit  of  the  Peak  of  Teneriffe, 
the  winds  are  almost  always  from  the  west,  or  in  a  direction  op- 
posite to  the  trade  wind  below. 

2.  Monsoons. — Owing  to  the  peculiar  configuration  of  the  land 
surrounding  the  Indian  Ocean,  the  trade  winds  are  subject  to 
some  modification.     Thus,  in  the  southern  part  of  this  ocean,  be- 
tween New  Holland  and  Madagascar,  the  southeast  trade  wind 
continues  during  the  whole  year ;  but  in  the  northern  part,  the 
wind  from  October  to  April  is  from  the  northeast,  and  from  April 
to  October  from  the  southwest.     These  are  called  monsoons.     A 
series  of  observations  are  in  progress  by  Professor  J.  H.  Coffin, 
which  promise  to  throw  much  light  on  the  direction  of  these  and 
other  winds. 

3.  The  Simoon,  a  hot  and  destructive  wind,  which  prevails  in 

Where  is  the  region  of  calms,  and  what  is  the  cause  ?  How  do  the  up- 
per trade  winds  move  ?  How  are  monsoons  produced  ?  Describe  the  si- 
moon and  its  cause. 


LAND    AND    SEA    BREEZES.  191 

the  deserts  of  Asia  and  Africa,  is  produced  by  the  air  becoming  in- 
tensely heated  over  the  sands  of  the  desert.  When  this  air  attains 
considerable  velocity,  it  takes  up  the  fine  sand,  which,  being  ex- 
ceedingly dry,  becomes  very  injurious  to  travelers  in  those  regions. 
There  are  also  very  dry  and  cold  winds,  called  the  Puna 
Winds,  which  prevail  on  the  high  table  lands  of  the  Cordilleras 
in  Peru. 

4.  Land  and  Sea  Breezes  are  due  to  the  unequal  action  of 
the  rays  of  heat  upon  the  land  and  water.     During  the  day  the 
land  and  sea  receive  equal  quantities  of  caloric  from  the  sun,  but 
the  land  becomes  more  heated  than  the  water,  and,  consequently, 
the  air  over  it  is  more  expanded  and  rises  up,  while  the  cooler  air 
from  the  sea  flows  in  to  maintain  the  equilibrium.     During  the 
night  the  earth  radiates  its  heat  more  rapidly  than  the  sea,  and 
as  it  grows  cooler,  the  atmosphere  is  condensed  and  flows  toward 
the  sea. 

These  changes  near  the  sea  are  very  grateful  during  the  warm 
season.  The  sea  breeze  does  not  set  in  till  near  midday  or  after, 
nor  the  land  breeze  till  after  midnight,  as  it  requires  some  time 
for  the  change  to  take  place.  Between  the  two  there  is  general- 
ly a  calm,  showing  that  there  is  an  equilibrium  in  the  tempera- 
ture of  sea  and  land. 

5.  Hurricanes  are  produced  by  the  meeting  of  opposite  cur- 
rents of  air,  and  by  upward  currents.     They  prevail  most  exten- 
sively in  tropical  latitudes.    They  have,  at  the  same  time,  a  rota- 
ry and  a  progressive  motion.     According  to  the  observations  of 
Mr.  Pvedfield,  the  Atlantic  hurricanes  originate  a  little  east  of 
the  Caribbean  Islands,  and  pass  in  a  northwest  direction  to  the 
tropic,  and  from  thence  their  course  is  northeast.     They  rotate 
in  a  direction  opposite  to  the  apparent  motion  of  the  sun.     South 
of  the  equator  they  observe  a  similar  law,  but  move  in  exactly 
opposite  directions,  passing  toward  the  southwest  till  they  arrive 
at  the  southern  tropic,  and  from  thence  toward  the  southeast, 
and  rotating  in  the  same  direction  with  the  sun. 

Explain  the  manner  in  which  land  and  sea  breezes  are  produced.  How 
are  hurricanes  produced  ?  Where  do  the  Atlantic  hurricanes  commence, 
and  what  is  their  course  ? 


192  NATURAL    PHILOSOPHY. 

All  our  northeast  storms  are  great  whirlwinds.  They  are 
spread  over  large  areas,  often  extending  for  thousands  of  miles. 
Their  velocity  varies  from  7  to  30  or  40  miles  per  hour,  and 
hence  the  mechanical  effects  which  they  produce  are  very  various. 

In  consequence  of  their  rotary  motion,  the  air  in  their  center 
becomes  rarefied,  and  that  on  the  edges  of  the  storm  condensed. 
If  the  center'  of  the  storm  pass  over  the  place  where  the  experi- 
ment is  tried,  the  barometer  will  rise  at  the  commencement,  will 
fall  at  the  middle,  and  rise  again  at  the  close  of  the  storm. 
The  wind,  also,  will  change  to  all  points  of  the  compass,  and 
hence  sailors  generally  know  when  they  pass  into  the  center  of 
the  whirlwind,  from  the  sudden  calm  which  exists,  called  the  lull 
of  the  tempest. 

6.  Tornadoes  are  whirlwinds  of  limited  extent,  in  which  the 
rotary  motion  becomes  so  violent  as  to  tear  up  trees,  overturn 
buildings,  and  level  every 'thing  in  their  course.    They  sometimes 
move  at  the  rate  of  60  miles  per  hour.     They  occur  mostly  in 
the  torrid  zone. 

The  rate  at  which  winds  move  is  very  various.  A  gentle 
breeze  moves  from  6  to  10  miles  per  hour ;  a  storm,  30  ;  a  tor- 
nado and  hurricane,  60  miles  per  hour. 

7.  Water  Spouts  result  from  whirlwinds  passing  over  water 
By  their  rotary  motion  they  take  up  the  water  in  a  large  column 
in  the  same  way  that  they  take  up  straws  and  light  bodies  on 
the  earth's  surface.    These  whirls  seem  to  originate  in  the  upper 

Fig.  159.  Fig.  160.  Fig.  161. 


What  are  our  northeast  storms?  How  do  they  affect  the  barometer? 
What  are  tornadoes?  At  what  rate  do  winds  move?  How  are  water 
spouts  formed  ? 


MOISTURE    OF    THE    ATMOSPHERE.  193 

regions  of  the  atmosphere.  They  are  conical  or  funnel-shaped. 
Sometimes  their  points  do  not  reach  the  earth.  Usually  they 
appear  in  the  form  of  a  dark  cloud,  as  in  Fig.  160,  which  comes 
down  to  the  water,  and  carries  up  a  column,  giving  a  loud  and 
hissing  sound,  due  to  the  violent  agitation  of  the  water  in  the 
whirling  spout.  The  forming  spout  is  represented  at  Fig.  159, 
the  spout  when  fully  formed  at  Fig.  160,  and  the  spout  as  it 
breaks  and  passes  away  in  Fig.  161. 

VI.  Moisture  of  the  Atmosphere. — The  atmosphere  contains 
variable  quantities  of  watery  vapor,  which  rises  up  from  evapo- 
ration. This  process,  which  is  very  active  in  warm  climates,  is 
carried  on  at  all  places  on  the  earth's  surface,  even  from  the  po- 
lar snows.  The  quantity  of  vapor  depends  simply  upon  the  tem- 
perature ;  and  as  the  temperature  becomes  rapidly  cooler  in  the 
upper  regions,  the  moisture  is  deposited  in  the  form  of  clouds, 
which  consist  of  hollow  vessels  of  water. '  When  these  unite  they 
produce  rain,  hail,  or  snow,  according  to  the  temperature  of  the 
region  and  the  circumstances  under  which  they  are  formed. 

The  quantity  of  watery  vapor  in  the  atmosphere  is  constantly 
varying,  and  the  amount  at  any  time  may  be  determined  by 
means  of 

Hygrometers. — These  are  of  several  kinds.  That  invented  by 
Saussure  depends  upon  the  property  which  the  human  hair  has 
of  contracting  when  dry,  and  lengthening  when  exposed  to  moist- 
ure. But  the  one  commonly  used  is 

DanielVs  Hygrometer,  which  depends  for  its  action  upon  the 
temperature  at  which  dew  is  formed,  called  the  Dew  Point.  If 
the  air  requires  to  be  cooled  but  slightly  before  it  will  deposit  dew, 
then  it  is  very  moist ;  if  it  require  to  be  cooled  a  number  of  de- 
grees before  the  dew  is  deposited,  it  is  dry. 

By  ascertaining,  then,  the  difference  between  the  temperature 
of  the  atmosphere  and  the  dew  point,  we  may  determine  the 
quantity  of  moisture  which  the  atmosphere  contains. 

Darnell's  hygrometer,  by  which  the  dew  point  is  ascertained, 

W  hat  causes  the  moisture  of  the  atmosphere  ?  What  condenses  it  ?  How 
is  the  quantity  determined  ?  Describe  the  principle  of  hygrometers.  De- 
scribe Daniell's  hygrometer. 


194 


NATURAL    PHILOSOPHY. 


Fig.  162. 


consists  of  a  tube  with  two 
bulbs,  a  b,  Figure  162.  The 
bulbs  are  free  from  air,  and  one 
of  them,  b,  made  of  black  glass, 
is  about  half  full  of  ether.  A 
thermometer,  d,  is  placed  in 
the  stem  c,  just  dipping  into  the 
ether,  to  ascertain  the  temper- 
ature of  the  bulb,  and  another 
thermometer  is  placed  on  the 
standard  to  measure  the  tem- 
perature of  the  air.  The  bulb 
a  is  covered  with  a  piece  of 
muslin.  Now,  on  pouring  upon 
a  a  small  quantity  of  ether,  it 
will  become  cool  by  the  evap- 
oration, and  the  vapor  of  ether 
within  it  will  be  condensed. 
This  will  remove  the  pressure 
from  the  ether  in  #,  and  it  will  evaporate,  absorbing  caloric  from 
the  bulb,  by  which  its  temperature  will  be  diminished.  The 
temperature  of  c  d  at  the  moment  that  dew  begins  to  form  on 
the  surface  of  the  black  glass  is  the  temperature  of  the  dew  point ; 
the  temperature  of  the  air  is  indicated  by  the  thermometer  on 
the  standard;  and  from  these  observations,  by  means  of  tables 
constructed  for  the  purpose,  we  can  determine  the  quantity  of 
moisture  in  the  atmosphere. 

Thus  it  has  been  found  by  experiment  that  in  35.3+  cubic 
feet  of  air,  at  a  temperature  of  172°  F.,  264*93  grains  of  water 
may  be  contained.  The  air  is  then  exactly  saturated  with  wa- 
ter, and  this  is  the  dew  point. 

Now,  by  repeating  the  experiment  for  each  degree  of  tempera- 
ture, and  ascertaining  the  quantity  of  water  which  the  35'3-f- 
cubie  feet  of  air  is  capable  of  containing,  we  may  construct  a  table 
by  which  the  quantity  of  moisture  in  the  atmosphere  at  any  given 
time  may  be  determined. 

As  the  quantity  of  water  in  the  atmosphere  depends  upon  the 
temperature,  there  is  more  in  the  summer  than  in  the  winter  ; 

What  is  the  dew  point,  and  how  does  it  show  the  state  of  the  atmosphere 
as  it  respects  its  moisture  ?  How  are  the  tables  made  out  to  ascertain  the 
quantity  of  water  in  the  atmosphere  by  the  hygrometer  ?  When  does  the 
Atmosphere  contain  most  moisture  ? 


DEWS — MISTS CLOUDS.  195 

though,  from  the  fact  that  the  heat  causes  the  warm  air  to  ascend 
to  a  greater  height  in  the  summer,  the  difference  near  the  surface 
is  not  easily  detected  ;  in  fact,  owing  to  the  greater  diffusion  of 
the  moisture,  the  air  is  generally  drier  in  summer  than  in  winter. 
The  absolute  quantity  of  water  is  at  its  minimum  in  January, 
and  at  its  maximum  in  July. 

The  quantity  also  varies  during  the  day.  As  the  heat  in- 
creases, larger  quantities  are  evaporated  ;  but,  owing  to  its  great- 
er diffusion,  it  is  drier  from  9  A.M.  to  4  P.M.  than  during  the 
remaining  24  hours. 

The  air  over  places  near  large  bodies  of  water,  as  the  sea-shore, 
generally  contains  more  moisture  than  that  in  the  interior  of  the 
country.  The  moisture  also  diminishes  in  going  from  the  equa- 
tor to  the  poles. 

1 .  Dew. — The  formation  of  dew  depends  upon  principles  al- 
ready stated.     The  earth  cools  during  the  night,  and  the  strata 
of  air,  saturated  with  moisture,  come  into  contact  with  the  cold 
earth,  and  a  portion  of  the  vapor  is  condensed.    As  all  bodies  do 
not  radiate  heat  with  equal  facility,  the  dew  will  be  deposited  un- 
equally.    Grass  and  leaves  cool  more  rapidly  than  mineral  sub- 
stances, and  hence  receive  a  greater  quantity  of  dew.     When 
clouds  are  formed,  they  impede  the  radiation  of  heat  from  the 
surface,  and  little  or  no  dew  is  deposited.     A  brisk  wind  also  in- 
terferes with  the  formation  of  dew  by  bringing  the  warm  cur- 
rents of  air  in  contact  with  the  surface. 

2.  Hoar-frost  is  frozen  dew.     Mist,  fog,  and  clouds  consist  of 
vesicles  of  water  suspended  in  the  air. 

3.  Mists  and  Fogs  are  produced  over  rivers  and  lakes  in  con- 
sequence of  the  difference  of  the  temperature  of  the  air.     When 
the  water  is  warmer  than  the  air  adjacent  to  it,  the  mingling  of 
colder  air  will  cause  a  deposit  of  fog ;  or  when  the  air  over  the 
water  is  colder  than  that  upon  the  land,  a  similar  deposit  takes 
place  by  the  intermingling  of  warm  and  cold  currents. 

4.  Clouds  are  nothing  but  mist  deposited  in  the  higher  regions 
of  the  atmosphere.     They  consist  of  small  hollow  vesicles  which 

How  does  the  moisture  vary  at  different  places  ?  What  is  the  cause  of 
devr— of  hoar-frost  ?  What  are  clouds  1 


196  NATURAL    PHILOSOPHY. 

are  a  little  heavier  than  the  air,  but  they  sink  very  slowly,  and, 
on  reaching  lower  strata,  they  are  dissolved  from  increase  of  tem- 
perature, and  are  borne  about  by  the  currents  of  air.  They  are 
constantly  forming  in  consequence  of  the  cold  and  warm  currents 
which  are  intermingling,  or  from  the  upward  currents  of  air,  which 
become  cooler  as  they  ascend,  and  deposit  their  moisture. 

This  is  the  reason  that  clouds  are  formed  on  the  tops  of  mount- 
ains. The  air,  in  passing  up  their  sides,  becomes  cooler,  arid  its 
moisture  is  deposited,  and  forms  a  cap  or  wreath  upon  their  summits 

Clouds  are  distinguished  by  several  epithets,  as  Feathery  Cirrus, 
which  are  the  highest ;  Cumulus,  which  are  more  dense ;  Stratus, 
consisting  of  horizontal  streaks  ;  Fleecy,  Rainy  or  nimbus,  &c. 

The  height  of  the  feathery  clouds  has  been  determined  in  some 
places  to  be  at  least  20,000  feet,  and  the  vertical  depth  of  some 
was  ascertained  to  be  from  1200  to  1400  feet. 

5.  Rain. — When,  by  the  condensation  of  vapor  in  the  atmos- 
phere, the  vesicles  of  mist  become  more  and  more  dense,  they  be- 
gin to  fall  rapidly,  and,  uniting  with  others  in  their  descent,  form 
into  drops,  which  descend  to  the  earth  in  showers  of  rain.  The 
formation  of  rain,  then,  is  precisely  similar  to  that  of  clouds  and 
mist,  the  mingling  of  cold  and  warm  currents  of  air. 

Quantity  of  Rain. — The  quantity  of  rain  which  falls  at  any 
place  during  the  year  may  be  determined  by  means  of  a  rain- 
gauge.  This  consists  of  a  cylinder  of  a  given  diameter,  in  which 
another  cylinder  is  placed  with  an  aperture  in  its  bottom,  through 
which  the  water  that  falls  may  pass  into  the  first  cylinder,  and 
the  quantity  measured  by  means  of  a  gauge  for  that  purpose. 

The  quantity  of  rain  varies  in  different  latitudes,  generally  de- 
creasing as  we  go  from  the  equator  to  the  poles.  There  is  also 
more  in  summer  than  in  winter.  Within  the  tropics  there  are 
alternate  seasons  of  rainy  and  dry  weather,  which  continue  from 
four  to  six  months  each.  Some  countries  are  so  situated,  as 
Egypt,  that  no  rain  ever  falls,  and  others  where  it  rains  most  of 
the  year. 

Why  do  they  form  and  disperse  so  rapidly?  Why  are  mountains  often 
capped  with  clouds  ?  Mention  the  different  kinds  of  clouds.  How  is  rain 
formed  ?  How  is  the  quantity  of  rain  which  falls  in  a  given  time  ascer- 
tained ?  What  variations  in  different  latitudes  ? 


RAIN SNOW HAIL.  197 

In  the  south  of  Europe  there  are  annually  about  120  rainy 
days ;  in  central  Europe,  146  ;  and  in  the  northern  portions, 
about  1 80  rainy  days.  But  the  quantity  does  not  depend  upon 
the  number  of  rainy  days ;  for,  though  the  number  increases  as  we 
go  north,  yet  the  quantity  of  rain  is  greater  near  and  within  the 
tropics. 

6.  Snow. — Snow  is  produced  by  the  condensation  of  vapor, 
but  exactly  how  the  flakes  are  formed  is  not  ascertained.     It  is 
probable  that  the  mist  is  not  in  the  form  of  vesicles,  but  of  small 
ice  crystals,  which  in  their  descent  enlarge  and  fall  in  snow-flakes. 
The  form  of  the  snow-flake  is  very  various,  yet  they  are  all  ref- 
erable to  a  hexagonal  star,  belonging  to  the  same  system  of  crys- 
tals as  quartz  or  the  rock  crystal.     These  forms  are  not  only  va- 
rious, but  exceedingly  beautiful,  especially  when  examined  by  a 
microscope. 

Snow  is  sometimes  colored  red  and  at  others  green.  This  is 
found  to  be  due  to  a  certain  species  of  plant,  a  fungus  which  has 
the  power  of  vegetating  in  the  region  of  eternal  frosts  and  snows 
with  the  same  luxuriance  that  other  plants  manifest  when  placed 
in  the  more  congenial  earth. 

7.  Hail  is  usually  formed  just  before  a  thunder  storm.     The 
stones  consist  of  a  nucleus  with  concentric  layers  of  ice.     It  is 
difficult  to  explain  exactly  how  they  can  be  retained  in  the  at- 
mosphere until  they  have  attained  so  large  a  size ;  some  have 
been  found  weighing  12  ounces.     Their  occurrence  is  attended 
with  very  sudden  changes  of  temperature,  and  also  with  thunder 
and  lightning. 

Volta  has  suggested  that  there  are  two  clouds  situated  above 
each  other,  and  the  hail  which  is  first  formed  in  the  upper  cloud 
falls  to  the  lower,  which  is  highly  electrified ;  then  the  stones,  be- 
coming also  electrified,  are  repelled,  and  sent  back  to  their  start- 
ing point,  and  thus  they  are  passed  back  and  forth  until  their 
size  becomes  so  great  that  they  fall  to  the  earth. 

It  is  difficult,  however,  to  conceive  how^  the  electricity  of  the 

What  is  snow,  and  how  is  it  formed?  What  is  the  cause  of  its  color? 
Under  what  circumstance*  is  hail  formed  ?  How  is  its  formation  explained  ? 
What  objection  to  Volta'i  theory? 


198  NATURAL    PHILOSOPHY. 

two  clouds  could  exert  such  a  force  without  passing  through  the 
air  and  forming  an  equilibrium,  which  of  course  would  destroy 
their  power  of  sustaining  the  hail  in  accordance  with  the  above 
theory.  There  is  no  doubt,  however,  that  hail  is  produced  by 
sudden  condensation  of  vapor,  in  connection  with  very  cold  strata 
of  air  through  which  it  falls.  The  size  of  the  stones  would  nat- 
urally increase  by  the  condensation  of  moisture  upon  their  sur- 
faces as  they  descend  toward  the  earth. 

VII.  Meteorolites. — The  atmosphere  is  the  occasion  of  phenom- 
ena, in  consequence  of  bodies  passing  through  it  or  undergoing 
changes  in  it,  which  have  been  described  under  the  terms  Fall- 
ing Stars,  Fire-balls,  arid  Meteoric  Stones. 

1.  Falling  Stars  are  so  called  because  they  resemble  stars, 
though  their  light  is  rather  more  diffused.     They  fall  through 
the  atmosphere  from  a  height  of  from  20  to  30  miles,  with  a 
velocity  of  15  or  20  miles  per  second. 

The  most  remarkable  circumstance  to  be  noticed  is,  that  they 
are  more. or  less  periodical,  the  periods  returning  annually  about 
the  13th  of  November  and  the  10th  of  August.  One  of  the 
most  remarkable  of  these  showers  of  stars  occurred  on  the  13th 
of  November,  1833,  in  which,  during  the  space  of  9  hours,  there 
fell,  according  to  calculation,  about  240,000  meteors.  They  ap- 
peared to  radiate  in  all  directions  from  a  point  a  little  south  of 
the  zenith,  and  flowed  down  like  flakes  of  snow  toward  the  hori- 
zon ;  some  of  them  passing  below  the  horizon,  and  others  going 
out  after  passing  a  short  distance  from  their  starting  point.  Va- 
rious theories  have  been  proposed  to  account  for  them,  but  their 
origin  is  not  yet  fully  known. 

2.  Fire-balls  appear  to  be  of  the  same  nature,  and  only  differ 
from  falling  stars  in  their  greater  size.     They  sometimes  appear 
as  large  as  the  full  moon,  and  pass  in  all  directions  through  the 
atmosphere.     They  explode  with  one  or  more  reports,  and  send 
down  to  the  earth  masses  of  matter  called  Meteoric  Stones,  which 
fall  with  great  velocity  and  bury  themselves  in  the  earth.    When 
first  fallen  they  are  very  hot,  and  exhibit  marks  of  fusion.     They 
have  a  peculiar  appearance  by  which  they  are  easily  distinguish- 

What  are  moteorolites,  falling  stars,  and  fire-balls  1 


METEOROLITES.  199 

ed.  They  generally  contain,  a  portion  of  native  iron  and  a  bitu- 
minous crust.  The  iron  is  not  always  pure,  but  alloyed  with  a 
small  quantity  of  nickel. 

3.  Stony  masses  have  been  found,  of  great  weight,  in  different 
parts  of  the  earth,  whose  origin  has  been  ascribed  to  the  same 
cause,  and  hence  are  called  Aerolites.  They  weigh  from  a  few 
ounces  to  several  hundred  pounds.  These  stones  appear  to  be 
solid  bodies  circulating  about  the  earth,  and  when  they  are 
brought  within  the  atmosphere,  their  great  velocity  compresses 
the  air,  and  its  latent  heat  becoming  developed,  gives  rise  to  the 
light,  heat,  and  consequent  explosion  which  usually  attend  their 
appearance.  By  this  means  a  portion  or  the  whole  of  the  mass 
is  precipitated  to  the  earth. 

The  Color  of  the  Atmosphere  is  due  to  the  refraction  and  re- 
flection of  light.  There  are  other  phenomena  of  the  atmosphere, 
such  as  halos,  the  rainbow,  thunder  and  lightning,  which  are  con- 
nected with  electricity  and  light,  and  will  be  better  understood 
in  connection  with  those  subjects. 

VIII.  Relations  of  the  Atmosphere  to  Animals  and  Vegeta- 
bles.— The  relations  of  the  atmosphere  to  organic  nature  are  most  t 
intimate  and  highly  important. 

Its  density  and  perfect  fluidity  are  such  that  animals  move  about 
in  it  without  any  sense  of  its  presence,  unless  it  is  in  rapid  mo- 
tion, and  yet  its  influence  is  constant,  and  absolutely  essential  to 
the  existence  of  animal  and  vegetable  life. 

1.  The  inhabitants  of  countries  situated  far  above  the  level  of 
the  ocean,  where  the  air  is  more  rare,  have  generally  larger  chests, 
in  order  to  obtain  the  requisite  quantity  of  oxygen.  On  ascend- 
ing high  mountains,  where  the  air  is  rare,  a  difficulty  is  often  ex- 
perienced in  respiration,  due  to  diminished  pressure  and  the  small- 
er quantity  of  oxygen ;  and  in  descending  in  a  diving-bell,  where  ^ 
the  air  is  compressed  by  a  column  of  water,  the  quantity  of  ox- 
ygen taken  into  the  lungs  increases  too  much  the  circulation. 
This  gives  an  increase  of  strength,  but,  if  continued  long,  is  in- 

Describe  the  meteoric  stones  and  the  manner  of  their  production  ?  To 
what  is  the  color  of  the  atmosphere  due  ?  What  are  the  relations  of  the  at- 
mosphere to  animals  ?  What  difficulty  do  persons  experience  in  ascending 
high  mountains  or  in  descending  in  a  diving-bell  ? 


200  .  NATURAL    PHILOSOPHY. 

jurious  to  health.  The  density  at  the  surface  seems  best  adapt- 
ed to  the  purposes  of  life. 

2.  Not  only  the  constitution  of  the  atmosphere,  but  its  com- 
position, is  such  as  to  adapt  it  to  the  structure  of  the  lungs  of  an- 
imals, and  to  the  important  changes  which  are  effected  through 
its  agency  upon  the  processes  of  life. 

The  atmosphere  consists  chiefly  of  about  21  parts  of  oxygen  and 
79  of  nitrogen  in  100.  The  oxygen  enters  the  lungs  of  all  air- 
breathing  animals  with  the  nitrogen,  and,  passing  into  the  circu- 
lation, combines  with  those  parts  of  the  body  which  have  served 
their  purpose,  and  must  be  ejected,  and  with  that  portion  of  the 
food  which  can  not  be  assimilated,  forming  carbonic  acid  and 
water.  These  substances  are  ejected  along  with  the  nitrogen  at 
each  expiration.  By  this  process  the  functions  of  life  are  sustain- 
ed. In  animals  living  in  the  water,  a  portion  of  air  is  conveyed 
through  the  medium  of  water  to  their  gills,  and  the  process  of 
purification  performed  in  a  similar  way. 

The  atmosphere  contains  variable  quantities,  as  we  have  seen, 
of  watery  vapor,  which  rises  up  continually  from  the  surface  of 
the  ocean  and  the  land,  and  is  precipitated  again  over  the  whole 
earth  to  supply  the  wants  of  organic  life. 

There  is  also  a  variable  quantity  of  carbonic  acid  in  the  at- 
mosphere, which  is  produced  by  several  causes,  such  as  the  respi- 
ration of  animals,  combustion,  decay,  arid  changes  going  on  among 
the  rocks.  This  acid  is  injurious  to  animals,  but  is  the  proper 
food  of  vegetables,  whose  leaves  and  roots  absorb  it,  appropriate 
its  carbon  under  the  influence  of  solar  light,  and  return  the  oxy- 
gen to  the  atmosphere  for  the  use  of  animals.  It  is  by  this  pro- 
cess that  the  purity  of  the  atmosphere  and  its  uniformity  of  com- 
position are  constantly  maintained.  As  the  oxygen  in  confined 
apartments  is  constantly  consumed  by  the  power  of  respiration, 
and  as  the  carbonic  acid  thus  produced  is  not  fit  to  support  respi- 
ration, it  becomes  necessary  to  remove  this  foul  air  by  some  me- 
chanical arrangements. 

IX.  Ventilation. — The  principle  upon  which  a  draught  is  pro- 

What  is  the  composition  of  the  atmosphere  ?  What  are  the  causes  which 
produce  carbonic  acid  in  the  atmosphere  ? 


VENTILATION.  201 

Wig.  163.  duced  in  a  chimney  may  be  illustrated  by  plac- 
ing a  lamp,  a  b,  Fig.  163,  in  a  tube.  The  com- 
bustion of  the  oil  in  a  b  will  not  only  consume 
a  portion  of  the  air,  but  heat  it  and  make  it  spe- 
cifically lighter  than  the  surrounding  air.  This 
lighter  air  will  be  forced  up  by  the  pressure  of 
j  the  more  dense  portions,  and  a  current  will  de- 
scend through  c  d  and  up  b  a.  The  chimney  is 
the  same  as  the  tube,  the  fire  is  the  lamp,  and  as  the  column  of 
air  in  it  becomes  heated,  the  air  of  the  room,  which  gains  access 
in  various  ways,  being  more  dense,  flows  through  the  fire,  and 
thus  a  constant  draught  is  kept  up.  It  requires  but  a  slight 
variation  of  temperature  to  determine  the  direction  of  the  cur- 
rent. 

The  air  in  the  chimney  must  therefore  be  lighter  than  that  in 
the  room,  or  the  draught  will  be  in  the  opposite  direction.  This 
is  often  the  case  when  a  fire  is  first  built.  The  external  air  be- 
ing more  dense  than  that  in  the  apartment,  a  current  of  air  flows 
down  the  chimney,  and  the  smoke  at  first  does  not  ascend ;  or 
the  chimney  may  be  so  large  that  a  sufficient  body  of  air  can  not 
be  heated  to  produce  an  upward  current,  and  in  this  case  the  fire 
will  smoke ;  or  the  room  may  be  too  tight,  so  that  air  can  not 
gain  admission  through  the  doors  or  windows,  and  in  that  case 
two  currents  may  be  established  in  the  chimney,  the  one  outward 
and  the  other  inward,  which  will  interfere  with  its  draught.  The 
chimney  may  be  too  broad  at  its  entrance,  or  too  high  from  the 
hearth,  or  too  short,  so  that  the  ascending  current  will  not  attain 
sufficient  velocity  to  counteract  the  external  pressure  of  the  cold- 
er air  from  its  top ;  or,  finally,  the  top  may  be  so  situated  as  to 
be  influenced  by  irregular  currents  of  air. 

To  remedy  these  defects,  the  chimney  may  be  contracted  at 
the  bottom  and  also  at  the  top.  The  heated  air  and  smoke  will 
then  attain  a  greater  velocity.  Or  its  height  may  be  increased. 
The  higher  it  is,  provided  it  is  not  too  large,  the  greater  will  the 
velocity  of  the  upward  currents  become.  Hence,  in  some  furna- 
ces and  manufactories,  where  a  strong  draught  is  requisite,  chim- 
neys are  made  very  high. 

What  is  the  principle  upon,  which  a  draught  is  formed  in  a  chimney? 
What  are  the  causes  which  interfere  with  the  draught  ? 

I  2 


202 


NATURAL    PHILOSOPHY. 


Fig.  165. 


Sometimes  one  chimney  enters  another  at  nearly    Fig,  164> 
right  angles,  and  in  this  case  the  draught  of  one  will 
generally  be  injured.     The  more  rapid  ascending  cur- 
rent will  interfere  with,  and  nearly  prevent  the  motion 
of  the  current  which  it  meets.     Thus,  if  we  take  two 
tubes,  a  b,  Fig.  164,  the  one  entering  the  other  at  near- 
ly right  angles,  if  the  current  in  the  tube  a,  produced  by 
a  strong  heat,  meet  the  current  in  b,  produced  by  a  less 
heat,  the  latter  will  be  overpowered  by  the  former  ;  or 
if  the  stronger  current  is  in  b,  that  in  a  will  be  over- 
come.    The  flues,  therefore,  should  enter  each  other  at 
a  very  acute  angle,  or,  rather,  there  should  be  separate  flues  for 
each  fire  carried  to  the  top  of  the  chimney,  and  then  their  cur- 
rents will  not  interfere. 

The  draught  of  a  chimney  may 
be  aided  by  mechanical  contriv- 
ance, and  by  the  form  given  to  its 
top.  We  may  assume  that  the 
"wind  will  strike  the  chimney  near- 
ly at  right  angles  to  the  direction 
of  the  smoke.  If,  therefore,  the 
top  is  conical,  and  slightly  con- 
tracted at  its  summit,  the  air,  strik- 
ing upon  the  sides  of  this  cone,  will 
bound  over  and  around  it,  Fig. 
165,  and  produce  a  partial  rarefac- 
tion, as  at  v,  which  will  have  a 
tendency  to  draw  the  smoke  up 
arid  increase  the  draught. 

Turncaps  have  also  been  ap- 
plied to  chimneys  to  increase  the 
draught,  which  we  will  more  es- 
pecially consider  in  pointing  out  the  methods  of  taking  out  foul 
air  from  apartments,  and  introducing  cold  or  warm  air  accord- 
ing to  the  season. 

In  a  room  where  a  number  of  individuals  remain  for  any  time, 
especially  in  public  halls  and  school-rooms,  the  draught  from  the 
chimney  is  not  sufficient  to  carry  off  all  the  foul  air  ;  and  partic- 
ularly is  this  the  case  when  rooms  are  heated  by  furnaces  or  tight 
stoves. 

How  should  flues  be  built?  In  what  other  ways  may  the  draught  be 
*ided? 


VENTILATION.  203 

In  such  cases  chimneys  may  be  built  in  the  walls,  or  tubes  in- 
troduced for  the  escape  of  the  vitiated  air.  In  order  to  promote 
this,  certain  arrangements  may  be  made  to  increase  the  draught. 

The  tubes  to  take  out  this  air  should  be  proportioned  to  the 
size  of  the  room  and  to  the  number  of  persons  who  may  be  in  it. 

The  arrangement  most  easily  made  is  to  have  a  chimney  built 
in  the  wall,  with  apertures,  c,  b,  Fig.  166,  one  near  the  top  and 
the  other  near  the  bottom  of  the  room.  Registers  fitted  to  these 
apertures  may  be  opened  or  closed  at  pleasure. 

The  object  of  this  is  to  close  the  upper  register  when  the  warm 
air  is  first  admitted,  as  it  will  rise  to  the  top  of  the  room,  and 
open  the  lower  register  to  allow  the  cold  air  to  escape  through  it ; 
but,  after  the  room  is  occupied  for  a  time,  the  impure  air  will  rise 
to  the  ceiling,  and  the  top  register  should  then  be  opened  to  let 
it  flow  out. 

The  draught  may  be  increased  by  fixtures  upon  the  top,  as  in 
the  case  of  an  ordinary  chimney. 

By  numerous  experiments  upon  turncaps  of 
various  forms,  that  represented  in  Fig.  166,  a, 
is  found  to  be  the  best ;  it  consists  of  a  tube, 
with  the  small  end  constantly  turned  toward 
the  wind  by  means  of  a  vane,  while  the  smoke 
A  passes  out  through  the  larger  end.  The  wind 

fl  "T 1     passes  over  the  mouth  of  the  chimney  through 

the  smaller  portion  of  the  tube.  By  this  action 
a  rarefaction  will  be  produced  upon  the  chim- 
ney,  which  will  be  greater  or  less  in  proportion 
to  the  force  of  the  wind,  and  the  draught  will 
thereby  be  increased. 

This  principle  is  similar  to  that  described  page  180.  As  the 
air  which  is  passing  through  the  smaller  end  is  constantly  ex- 
panding through  the  larger,  it  draws  up  the  air  from  the  chim- 
ney to  fill  the  partial  vacuum  thus  occasioned. 

A  ventilator  has  been  lately  invented5*  which  combines  the 
principle  of  the  cone  with  some  additions.  This  is  said  to  be 

*  Patented  by  F.  Emerson,  Esq.,  Boston. 

How  should  the  registers  be  arranged  ?  When  should  they  be  opened, 
and  when  closed  ? 


204  NATURAL    PHILOSOPHY. 

very  effective  for  increasing  the  draught  of  chimneys.     The  fol- 
lowing is  a  representation  of  it : 

It  consists  of  a  tube,  c,  Fig.  167,  inserted  in  Fig  167 

the  top  of  the  chimney,  upon  which  there  is 
mounted  a  cap,  a,  like  the  frustum  of  a  cone, 
with  a  plate,  b,  at  a  small  distance  from  the 
opening,  to  prevent  air  and  rain  from  entering  the 
chimney.  For  the  purpose  of  introducing  pure 
air,  an  injector  is  employed. 

When  we  remember  that  each  individual  in 
an  apartment  consumes  or  renders  unfit  for  res- 
piration about  12  cubic  feet  of  air  per  hour,  it 
becomes  obvious  that  in  a  crowded  hall  a  large 
quantity  of  pure  air  should  be  introduced,  and  that  the  means  of 
expelling  that  which  is  impure  should  be  most  ample.  But  this 
is  not  all.  The  lights  in  the  room  also  consume  oxygen  and  pro- 
duce carbonic  acid.  Watery  vapor  and  carbonic  acid  also  flow 
into  the  room  from  perspiration  and  from  respiration,  so  that 
each  individual  should  have  at  least  16  cubic  feet  of  pure  air 
per  hour. 

Pure  air  is  better  if  taken  from  the  top  of  the  building,  and  in- 
troduced by  means  of  tubes  through  numerous  apertures  in  the 
room,  as  thereby  it  is  more  equally  diffused,  and  cold  and  hot 
currents,  which  are  highly  injurious  to  health,  are  prevented. 

The  proper  ventilation  of  the  hold,  cabins,  and  timbers  of  a 
ship  is  an  object  of  great  importance.  The  plan  of  Mr.  Emer- 
son, in  the  use  of  his  "corresponding  ventilators"  the  injector 
and  ejector  for  the  hold  and  cabins,  as  above  described,  is  said  to 
be  very  effective.  We  have  lately  seen  a  plan*  for  ventilating 
the  timbers  of  a  ship  which  appears  to  be  both  practicable  and 
effective.  Between  the  ribs  of  a  ship  there  is  an  open  space, 
produced  by  the  planking  on  the  outside  and  the  ceiling  on  the 
inside  of  the  vessel ;  and  near  the  keel  water  always  accumu- 
lates, called  bilge  ivater,  which  not  only  becomes  very  offensive 
and  injurious  to  health,  but,  added  to  the  foul  atmosphere,  causes 
*  Patented  by  Captain  Knight,  Ne  7f  York. 

How  much  pure  air  ought  each  individual  to  have  per  hour?  Describe 
the  process  of  ventilating  the  timbers  of  a  ship. 


UNDULATIONS.  205 

the  decay  of  the  timbers.  This  space  between  the  timbers  is 
usually  closed  at  the  top  by  the  plank  sheer  or  railing,  and  at  in- 
tervals by  salt  stops.  Now,  if  apertures  were  made  through  the 
railing  and  salt  stops,  so  that  the  air  could  circulate,  this  water 
would  be  less  offensive  and  destructive. 

Ftff.168.  Thus,  let  Fig.  168  represent  two  ribs  of  a 

ship,  and  a  b  bilge  water.     As  the  ship  always 
rolls  more  or  less  at  sea,  the  water  will  be 
thrown  up  on  one  side,  b  d,  forcing  out  the  im- 
C\\.  ^/d  Pure  air>  and  the  Pure  air  will  flow  down  on 

the  other,  c  a.     By  flowing  down  on  each  side 
alternately,  pure  air  is  made  to  circulate,  and 
to  keep  the  water  from  becoming  stagnant. 

Pure  air  is  often  introduced  into  the  hold  of  a  vessel  by  meana 
of  a  sail,  made  into  a  conical  form.  But  we  must  refer  the  stu- 
dent to  works  which  treat  of  ventilation  for  a  fuller  view  of  the 
subject. 


CHAPTER  V. 

OF   UNDULATIONS. 

L  There  is  a  class  of  motions  called  undulations,  which  arise 
from  any  disturbance  among  the  ato?ns  of  an  elastic  substance. 
The  causes  of  undulatory  motions  are  gravity  and  elasticity. 
Undulations  are  progressive  and  stationary. 

II.  1.  The,  number  of  vibrations  of  an  elastic  rod  is  inversely 
as  the  square  root  of  its  length,  and  the  vibrations,  whether  larg- 
er or  smaller,  are  all  performed  in  the  same  time. 

2.  The  vibrations  of  a  stretcJied  cord  are  also  isochronous. 
But  the  number  in  a  given  time  increases  with  the  tension  of 
the  string  ;  it  is  as  the  square  root  of  the  stretching  weight,  and 
with  a  given  tension  is  inversely  as  the  length  of  the  string. 
When  strings  of  the  same  material  but  of  different  thickness  are 
compared,  the  number  of  vibrations  is  inversely  as  their  diame- 
ters. Vibrating  strings  are  disposed  to  divide  themselves  into 
definite  parts,  ivith  points  of  rest  called  nodes. 


206  NATURAL    PHILOSOPHY. 

3.  Elastic  planes,  when  made  to  vibrate,  divide  themselves 
into  parts  with  nodal  lines,  and  observe  the  same  laws  as  vibrat- 
ing rods. 

III.  Undulations  in  liquids,  or  water  waves,  are  generally 
produced  by  air  and  gravity.     They  have  a  progressive  motion, 
due  to  the  rising  and  sinking  of  the  particles  of  water  in  a  ver- 
tical plane.     When  they  fall  upon  surfaces  they  are  reflected, 
and  interfere  with  each  other,  producing  standing  vibrations. 
W^hen  two  si/stems  encounter  each  other,  they  may  produce  par- 
tial or  total  interference,  or  unite  and  form  a  wave  of  greater 
'magnitude. 

IV.  1.  Waves  are  produced  in  the  air  by  any  disturbance  of  its 
density.    An  air-wave  consists  of  a  rarefied  and  condensed  por- 
tion.    Their  length  depends  upon  the  number  of  vibrations  in 
a  given  time,  and  their  intensity  upon  the  degree  of  condensa- 
tion; but,  wliether  feeble  or  intense,  all  air -waves  move  with  the 
*ame  velocity. 

2.  Air -waves  are  reflected,  interfere  with  each  other,  form 
nodes  of  vibration,  and  have  a  definite  relation  to  the  length  of 
pipes  in  which  they  may  be  formed. 

IN  treating  of  motion  and  its  laws,  we  have  omitted  to  consider 
a  class  of  motions  which,  from  their  peculiar  character,  are  call- 
ed undulations,  and  also  vibrations. 

Undulations  consist  of  a  tremulous  motion,  which  passes  in  a 
vibratory  or  wave-like  manner  through  some  elastic  medium. 

When  such  motions  take  place  through  the  medium  of  solid, 
liquid,  or  gaseous  bodies,  they  give  rise  to  different  waves,  as  wa- 
ter-waves, waves  of  sound,  musical  tones,  &c.  ;  and  when  simi- 
lar motions  take  place  in  what  is  called  the  ether,  a  substance 
which  is  now  believed  to  pervade  all  matter  and  to  extend 
throughout  space,  they  are  supposed  to  give  rise  to  the  phenom- 
ena of  light,  heat,  and  possibly  to  electricity. 

A  knowledge,  therefore,  of  the  origin,  laws,  and  effects  of  such 
undulatory  movements,  is  highly  important  in  order  to  a  full 

What  are  undulations,  and  how  are  they  produced  ?  To  what  do  they 
give  rise  ? 


UNDULATIONS.  207 

comprehension  of  the  remaining  branches  of  Natural  Philoso- 
phy- 

I.  Origin  of  Undulations. — Undulations  arise  from  any  dis- 
turbance among  the  atoms  of  an  elastic  substance.  This  disturb- 
ance may  have  a  great  variety  of  causes,  as  a  sudden  blow  or 
impulse.  Chemical,  mechanical,  or  any  other  force  which  is 
capable  of  acting  upon  matter  may  give  rise  to  it. 

But,  whatever  be  the  cause  of  this  disturbance,  the  undulations 
themselves,  in  the  three  forms  of  matter  which  we  have  consid- 
ered, depend  either  upon  elasticity  or  gravity,  or  upon  both  unit- 
ed ;  ibr  one  or  both  of  these  forces,  which  constantly  strive  to  re- 
store the  disturbed  parts  to  a  state  of  rest,  are  essential  to  the 
commencement,  and  the  sole  causes  of  the  continuance  of  undu- 
latory  motion. 

Undulations  are  either  stationary  or  progressive. 

1.  Stationary  Undulations  are  those  which  are  performed 
when  all  the  parts  of  a  vibrating  body  simultaneously  swing  back 
and  forth  within  certain  limits  in  exactly  the  same  time,  as  is 
exemplified  in  the  pendulum  of  a  clock,  or  in  a  string  fastened  at 
the  two  extremities,  and  motion  given  to  it  by  pulling  the  middle 
to  one  side,  and  then  leaving  it  to  exert  its  elastic  force.     The 
vibrations  of  such  a  string  are  also  said  to  be  transverse. 

2.  Progressive  Undulations  are  such  as  are  formed  on  the  sur- 
face of  water  when  it  becomes  agitated  by  the  wind,  or  such  as 
are  produced  by  a  cord  fastened  at  one  end,  while  the  other  end 
is  moved  up  and  down,  until  a  wave-like  motion  is  given  to  it. 
There  is,  however,  no  progressive  motion  of  the  parts  of  the  cord 
or  of  the  particles  of  water,  but  a  successive  rising  and  falling  in 
the  same  plane.     This  is  shown  in  water  waves  by  the  fact  that 
light  bodies  floating  on  the  surface  of  water  are  not  carried  along 
in  the  direction  in  which  the  wave  is  moving,  but  simply  rise  and 
fall  as  the  wave  passes  under  them.    When  the  wave  has  reached 
its  limit,  it  returns  with  an  inverted  motion,  and  continues  to  pass 
back  and  forth  until  all  the  parts  are  restored  to  a  state  of  rest. 

What  is  the  origin  of  undulations  ?  What  are  the  causes  of  this  disturb- 
ance ?  What  are  stationary  undulations  ?  transverse  ?  What  are  progress- 
ive undulations  ? 


208  NATURAL    PHILOSOPHY. 

Thus,  in  Fig.  169,  we  have  D          &*• 

a  representation  of  the   pro-  j  m  J>>^--r- 
gressive    undulations    of    the  P 


one  wave  length,  passing  from  nw  -  **"       *s*-^__—  ^  6 

left  to  right,     m  D  n  is  the 

elevation,  n  E  o  the  depres-  Him  -  -  iZZZZ^s^^^t 

sion,  j9  D  the  height,  and  q  E 

the  depth  of  the  wave.     Nos.  -p^  /^*L^  --  "^f 

I.,  II.,  represent  the  success- 

ive positions  of  the  advancing  *-*.  ___  -^  _ 

wave  from  left  to  right,  and         "<-  —  ' 

III.,  IV.,  V.,  those  of  its  return  from  right  to  left. 

Both  standing  and  progressive  undulations  may  take  place  in 
liquids  and  gases  as  well  as  in  solids.  Let  us  now  proceed  to 
examine  the  laws  which  govern  them  in  each  of  the  three  forms 
of  matter. 

II.  Laivs  of  Undulations  in  Solids.  —  For  the  purpose  of  ex- 
hibiting the  laws  of  vibration  in  solids,  we  may  divide  them  into 
rods,  strings,  planes,  and  masses. 

1.  Rods.  —  In  the  vibrations  of  a  pendulum,  all  the  particles  of 
which  it  is  composed  maintain  their  position  in  reference  to  each 
other  unchanged  ;  but  if  a  steel  spring  or  elastic  rod,  which  is 
fastened  at  one  end,  is  bent  in  any  direction,  its  particles  are 
slightly  disturbed,  and  tend  to  restore  themselves  by  the  force  of 
their  elasticity  ;  but  in  the  effort  to  regain  a  state  of  equilibrium, 
they  cause  the  free  portion  of  the  spring  to  make  a  series  of  vi- 
brations, which  grow  less  and  less  until  the  whole  is  brought  to  a 
state  of  rest.  In  this  case  we  may  notice  the  motion  of  the 
spring  as  a  whole,  which  is  similar  to  that  of  a  pendulum  — 
with  the  exception  that  the  motion  of  the  top,  Fig.  170, 
is  sometimes  curvilinear,  as  is  shown  when  a  bead  is  fasten- 
ed upon  the  end  of  a  steel  rod  —  and  also  the  motions  of  the 
individual  particles  which  compose  it.  All  the  parts  of 
the  rod,  and  each  separate  particle,  pass  back  and  forth  in 
the  same  time,  though  the  amplitude  of  their  motion,  or 
the  distance  they  pass  on  each  side  of  their  line  of  rest,  is 

Illustrate  by  the  diagram.  How  do  vibrating  rods  differ  from  the  pen- 
dulum ? 


UNDULATIONS    OF    STRINGS.  209 

very  different.     The  passage  of  the  rod  back  and  forth  is  called 
a  vibration. 

(I.)  The  number  of  vibrations  which  a  steel  rod  will  execute 
in  a  given  time  is  inversely  as  the  square  root  of  its  length. 
Thus  a  rod  which  will  make  16  vibrations  in  a  second,  will 
make  four  times  as  many,  or  64  vibrations,  in  the  same  time,  if 
reduced  to  one  half  of  its  length,  and  but  one  quarter  as  many, 
or  4,  if  its  length  is  doubled. 

(2.)  A  rod  thus  fastened  at  one  end  performs  all  its  vibrations 
in  exactly  the  same  time.  In  this  respect  the  law  is  the  same 
as  that  of  the  pendulum  (page  102). 

2.  Strings. — The  vibrations  of  strings,  whatever  their  mate- 
rial may  be,  are  generally  transverse.  That  is,  the  string  is 
stretched  between  two  fixed  points,  and  its  motion  takes  place  on 
each  side  of  the  line  of  rest. 

Jflfr.m.  Thus,  let  a  b,  Fig.  171,  be 

a  stretched  cord  or  wire,  and 
the  point /drawn  out  to  d,  and 
then  let  go  ;  it  will  perform  a 


series  of  vibrations  between  c 
and  d.  This  effect  is  due  to  its  elasticity ;  for,  when  it  has  ar- 
rived at/,  its  inertia  will  carry  it  to  c,  its  elasticity  will  bring  it 
back  again  to/,  and  then  its  inertia  will  carry  it  to  d  again. 
These  vibrations  will  be  continued  until  the  resistance  of  the  air 
and  the  slight  friction  at  the  ends  destroy  its  motion  or  bring  it 
to  a  state  of  rest.  It  will  be  noticed  that  all  the  parts  of  the 
string  reach  their  maximum  distance  on  each  side  of  the  line  of 
rest,  a  b,  and  pass  this  line  at  the  same  moment.  The  motion 
from  d  to  c  and  back  again  to  d  is  one  vibration ;  c  d  is  the  am- 
plitude or  intensity  of  the  vibration. 

The  vibrations  of  stretched  strings  are  governed  by  the  four 
following  laws  : 

(1.)  The  vibrations  of  a  stretched  cord,  whatever  be  their  am- 
plitude, are  performed  in  equal  times.  The  reason  of  this  law 
is  similar  to  that  given  for  the  oscillations  of  the  pendulum  (page 
102) ;  for,  the  greater  the  amplitude  of  the  vibrations,  the  greater 
the  velocity  of  the  several  parts  of  the  string ;  or,  in  the  longer 

What  is  the  law  of  vibration  in  an  elastic  rod  ?  How  do  strings  vi- 
brate ?  Mention  the  four  laws  which  govern  the  vibrations  of  a  stretched 
cord. 


210 


NATURAL   PHILOSOPHY. 


vibrations,  the  velocity  is  so  much  greater  than  it  is  in  the  short- 
er, that  they  are  performed  in  the  same  length  of  time. 

(2.)  The  number  of  vibrations  in  a  given  time  increases  with 
the  tension  of  the  string,  and  is  as  the  square  root  of  its  elastic 
force,  or  stretching  weight.  Thus,  if  the  stretching  weights  are 
made  4,  9,  and  16  times  as  great,  then  the  number  of  vibrations 
will  be  as  the  square  roots  of  these  numbers,  or  2,  3,  and  4  times 
as  many  in  the  same  time. 

(3.)  The  number  of  vibrations  of  a  string  is  inversely  as  its 
length.  That  is,  if  the  string  of  a  violin  or  any  other  instrument 
make  a  given  number  of  vibrations  per  second,  then,  if  the  ten- 
sion remain  the  same,  it  will  make  twice  as  many  vibrations  if 
but  half  of  the  string  is  allowed  to  vibrate  ;  3,  4,  and  5  times  as 
many  if  the  vibrations  are  performed  by  £d,  £th,  or  £th  of  the 
whole  length  of  the  string. 

(4.)  The  number  of  vibrations  of  different  strings  of  the  same 
'material  is  inversely  as  their  thickness  or  diameter.  Thus,  if  a 
wire  Y^o-th  of  an  inch  in  diameter  make  32  vibrations  per  sec- 
ond, another  wire  of  the  same  material,  which  has  twice  the  di- 
ameter, under  the  same  tension  will  vibrate  but  half  as  fast,  or 
16  per  second,  while  a  wire  whose  diameter  is  but  half  the  form- 
er will  perform  double  the  number  of  vibrations,  or  64  per  second. 

There  are,  however,  three  kinds  of  vibration  which  a  stretch- 
ed cord  or  wire  may  be  made  to  perform. 
Thus,  let  a  twisted  wire  be  suspended,  as  in 
Fig.  172,  and  stretched  by  means  of  a  heavy 
ball.  If  the  lower  end  is  secured,  it  will 
execute  transverse  vibrations ;  if  the  ball 
be  raised  up  and  let  fall,  its  vibrations  will 
be  longitudinal ;  and  if  it  be  twisted  and 
then  left  to  move,  its  vibrations  will  be  ro- 
tary. 

Nodes  and  Standing   'Vibrations. — A 
stretched  string,  during  its  vibrations,  will, 
under  certain  circumstances,  divide  itself  into  two  or  more  parts, 
which  have  a  definite  ratio  to  its  length.     Thus,  if  we  take  a 
How  are  transverse,  longitudinal,  and  rotary  vibrations  produced  1 


Fig.  172. 


UNDULATIONS    OF    SOLIDS. 


211 


small  cord,  and  stretch  it  between  two  fixed  points,  and  then, 
cause  it  to  vibrate  by  pulling  it  to  one  side  at  a  point  one  sixth 
of  its  length  from  the  end,  we  may  see  its  vibrations,  and  that 
there  are  one  or  more  points  of  the  cord,  at  equal  distances  from 
Fig  ns  each  other,  which  are  at  rest,  as  m  n,  Fig. 

173.  These  points  of  rest  are  termed 
nodes,  and  the  swelling  of  the  string  be- 
tween the  nodes  bellies.  These  nodes  may  be  readily  formed  by 
drawing  a  violin  bow  across  a  tensely-stretched  string  at  differ- 
ent points.  Sometimes  several  nodes  may  be  formed  at  equal 
distances  from  each  other,  giving  rise  to  standing  vibrations  be- 
tween each  node.  If  we  examine  the  lengths  of  the  vibrating 
parts,  we  shall  find  that  they  are  ?,  ^d,  £th,  &c.,  of  the  length  of 
the  string,  and  hence  that  the  number  of  their  vibrations  are  2, 
3,  and  4  times  as  many,  in  the  same  time,  as  would  be  performed 
if  the  whole  length  of  the  string  were  made  to  vibrate. 

An  elastic  rod,  also,  when  fixed  at  one  end,  divides  itself  into 
Fig.  174.  two  or  more  parts.     Thus,  if  the  rod 

a^ c'  —  —  c  —  ft  a  b,  Fig.  174,  is  fixed  at  a,  and  made 

to  vibrate,  it  will   divide  itself  into 

parts,  with  nodes,  c'  c.  The  parts  a  c1  and  c'  c  are  equal,  but  c 
b  is  but  half  as  long  ;  that  is,  the  distance  from  the  free  extrem- 
ity to  the  first  nodal  point,  c,  is  but  half  that  between  any  two 
nodal  points,  as  c  c'. 

3.  Planes,  Discs,  &c. — Elastic  planes,  whatever  their  form,  as  a 
plate  of  glass  or  metal,  may  be  made  to  vibrate  in  several  ways. 
175-  The  best  way  is  to  fasten  them  firm- 

ly by  means  of  a  vice,  and  then  to  draw 
a  bow  across  their  edges.  A  plate  thus 
B  fixed  may  be  thrown  into  a  series  of 
vibrations,  and  if  some  black  sand  be 
sprinkled  over  the  plate,  it  will  arrange 
itself  as  in  the  accompanying  figure 
(175).  The  lines  where  the  sand  col- 
lects are  termed  nodal  lines,  which  di- 

What  are  nodes,  and  how  may  they  be  produced?  What  is  meant  by 
standing  vibrations?  How  may  elastic  planes  be  made  to  vibrate  ?  How 
are  the  nodal  lines  shown  ? 


212 


NATURAL    PHILOSOPHY. 


vide  the  plate  into  spaces,  any  two  adjacent  spaces  being  in  op- 
posite states  of  vibration,  as  shown  by  the  signs  -f-  and  — . 

If  we  examine  these  lines  and  spaces,  we  find  that  those  at 
the  ends  are  but  half  the  size  of  those  in  the  centre ;  hence  the 
plate  is  similar  to  a  vibrating  rod,  and  may  be  regarded  as  com- 
posed of  a  series  of  rods  simultaneously  thrown  into  a  state  of 
vibration. 

The  form  of  the  figures  which  a  plate  is  capable  of  producing, 
or  the  manner  in  which  it  divides  itself,  will  depend  upon  its 
form,  the  point  of  support,  the  part  across  which  the  bow  is 
drawn,  and  the  point  which  is  touched  by  the  finger  during  its 
oscillations. 

By  varying  these  conditions,  we  may  produce  what  have  been 
termed  by  Chladni,  their  discoverer,  Sound  Figures. 

Thus,  let  #,  Fig.  176,  be  the  point  at  which  the  several 


plates  from  I.  to  II.  are  fastened  by  the  screw  of  the  vice,  b  the 
part  of  the  edge  across  which  the  bow  is  drawn.  The  sand  will 
then  be  arranged  on  the  nodal  lines,  which  are  in  a  state  of  re- 
pose, exhibiting  different  sound  figures. 

If,  however,  one  plate,  as  V.,  be  fastened  at  the  point  a,  while 

What  relation  do  the  spaces  bear  to  each  other?     Describe  the  process 
by  which  different  sound  figures  may  be  formed. 


UNDULATIONS    OP    LIQUIDS.  213 

the  finger  is  placed  at  w,  and  the  bow  drawn  across  the  edge  at 
b,  the  nodal  lines  represent  figures  which  appear  to  be  a  combi- 
nation of  all  the  preceding. 

If  the  plate  is  circular  and  fastened  at  its  center,  and  a  bow 
drawn  across  any  part  of  its  edge,  while  the  finger  is  placed  at 
45°  from  it,  the  figure  will  be  in  the  form  of  a  cross,  No.  III.  ; 
but  if  the  finger  be  placed  at  60°,  30°,  or  90°  from  the  point 
where  the  bow  is  applied,  the  nodal  lines  will  give  a  figure  of  six 
rays,  as  in  IV. 

It  will  be  seen  that  the  vibrations  in  the  above  rectangular 
planes  are  transverse;  that  is,  perpendicular  to  the  plane. 

The  laivs  of  vibrating  planes  are  the  same  as  those  of  vibrat- 
ing rods. 

III.  Undulations  of  Liquids.  Water- Waves. — 1.  Water- 
waves  are  generally  produced  by  the  combined  agency  of  air  and 
gravity  ;  but,  whatever  the  disturbing  cause  may  be,  any  eleva- 
tion or  depression  of  the  surface  of  a  liquid  is  propagated  to  a 
considerable  distance  from  the  point  of  disturbance.  Thus,  if  a 
stone  be  thrown  into  a  pond  of  water,  circular  waves  will  be 
formed,  which  consist  of  elevations  and  depressions,  that  follow 
each  other  with  considerable  rapidity,  and  spread  themselves  with 
uniform  velocity  to  a  greater  or  less  distance  over  the  surface  of 
the  pond. 

Such  waves  have  a  progressive  motion,  but  the  water  does  not 
move  in  the  direction  of  the  wave,  but  only  rises  up  and  down  in 
a  vertical  plane.  That  there  is  no  progressive  motion  of  the  wa- 
ter is  shown  by  the  fact  that  light  bodies  floating  upon  its  sur- 
face do  not  advance  with  the  wave,  but  only  rise  and  fall  in  a 
vertical  line  as  the  wave  elevations  and  depressions  pass  under 
them.  The  force  which  propels  the  wave  is  gravity.  The  par- 
ticles on  the  top  of  the  wave  are  drawn  down  by  this  force  with 
such  velocity  that  they  sink  below  the  general  level  of  the  sur- 
face, and  cause  the  particles  which  are  adjacent  in  the  advance 
of  the  wave  to  rise  up  and  form  another  elevation,  and  gravity 
again  draws  them  down  and  makes  a  second  depression.  Hence, 

How  are  water-waves  produced  ?  What  is  the  cause  of  their  motion  ? 
Does  the  water  advance  with  the  wave  ?  How  is  this  proved  ? 


214  NATURAL    PHILOSOPHY. 

after  one  elevation  or  depression,  the  force  of  gravity,  which  con- 
stantly strives  to  restore  all  the  particles  to  a  horizontal  plane, 
causes  them  to  perform  a  series  of  oscillations  in  vertical  planes 
at  right  angles  to  the  surface. 

In  order,  however,  to  understand  the  laws  of  water  undula- 
tions, we  must  examine  the  connection  of  the  wave  with  the  mo- 
tion of  the  separate  particles  of  water  concerned  in  its  propaga- 
tion. 

As  soon  as  the  wave  begins  to  move,  the  particles  of  water  on 
its  surface  begin  to  describe  curves,  which  return  into  themselves, 
and,  if  the  undulations  are  very  regular,  the  curve  is  a  circle. 
Each  particle  completes  one  entire  revolution  in  its  own  circle 
during  the  time  of  passing  from  its  highest  to  its  lowest  point  of 
vibration  and  back  again,  or  during  the  time  it  is  passing  from  the 
surface  above  and  below,  and  returning,  to  the  point  from  which 
it  commenced  its  motion ;  and  the  distance  the  wave  advances 
during  one  revolution  determines  the  length  of  the  wave,  and  the 
distance  that  each  particle  rises  and  sinks  is  its  intensity  or  am- 
plitude of  vibration. 

Thus,  let  there  be  a  row  of  eight  particles  on  the  surface  of  a 
liquid,  Fig.  177,  and  a  wave  pass  in  the  direction  of  the  arrows 
from  left  to  right. 

Fig.  177. 


Suppose  that  the  particle  a,  which  lies  upon  the  surface,  is  at 
rest  when  the  descending  wave  strikes  it.  It  will  be  depressed, 
and  begin  to  revolve  in  a  vertical  circle,  its  radius  assuming  the 
different  positions  represented  in  a  b  c  d,  &c.,  to  on,  during  the 
time  of  one  oscillation.  Now,  if  we  consider  eight  such  particles 
to  be  situated  on  the  line  a  m,  as  a  b  c,  &c.,  and  that  each  particle 
begins  its  motion  one  eightn  of  a  revolution  later  than  the  preced- 
ing, during  the  time  that  a  is  completing  one  revolution  each  suc- 
ceeding particle  will  move  through  a  portion  of  its  circle.  When 
a  has  passed  through  one  eighth  of  its  circle,  b  begins  to  move, 

What  motions  do  the  particles  of  water  make  ?  How  is  the  length  of 
the  wave  determined  ?  Illustrate  by  figure. 


REFLECTION    OF    WATER-WAVES.  215 

and  when  a  has  completed  an  entire  revolution,  m  begins  its  mo- 
tion. The  particles  between  a  and  m  are  in  the  condition  repre- 
sented in  7,  6,  5,  4,  &c. ;  that  is,  when  m  commences,  h  has  com- 
pleted jth,  g  fths,  /  fths,  e  f ths,  d  fths,  c  |ths,  b  Jths,  and  a 
one  entire  revolution.  The  particles  a  and  m  are  in  the  same 
condition,  and  the  line  which  joins  them  is  the  length  of  the 
wave,  and  lies  upon  its  surface.  The  diameter  of  the  circle 
which  each  particle  describes  is  the  amplitude  or  intensity  of  the 
wave,  c  6  its  depth,  and  g  2  its  height,  each  of  which  is  equal 
to  the  radius  of  the  circle  which  any  particle  describes  during 
one  oscillation.  This  radius  is  longer  or  shorter  according  to  the 
amplitude  of  the  wave.  It  is  sometimes  20  feet,  which  makes  a 
very  high  wave,  perhaps  the  largest  which  ever  occurs  on  the 
ocean  in  a  violent  storm,  unless  it  be  in  cases  where  one  wave 
mounts  upon  another  in  a  manner  which  we  shall  presently  ex- 
plain ;  but  the  power  of  the  wind  is  not  believed  to  extend  more 
than  20  feet  below  the  surface,  and  hence  waves  are  not  in  real- 
ity so  high  as  they  appear  to  be,  since  they  rarely  reach  an  am- 
plitude of  40  feet. 

2.  Reflection  of  Water-Waves. — When  the  undulations  of 
water  fall  upon  any  solid  surface,  they  are  reflected,  and  return 
in  paths  which  depend  upon  the  direction  in  which  the  incident 
wave  meets  the  reflecting  surface.  Thus,  if  we  consider  a  line 
of  particles  proceeding  from  the  origin  of  the  wave  in  the  direc- 
tion of  its  motion,  called  a  ray  of  undulation,  we  shall  find, 

(1.)  If  it  fall  upon  a  plane  surface  perpendicular  to  the  sur- 
face, it  will  be  reflected  and  return  in  the  same  path. 

(^*)  ^  ^  ^a^  uPon  tne  surface  at  any  angle,  as 
at  c,  in  the  direction  d  c,  Fig.  178,  it  will  be  reflect- 
ed  in  the  direction  c  a,  and  the  angle  which  the 
incident  ray  d.c  makes  with  a  perpendicular  to  the 
surface,  c  b,  is  equal  to  that  which  the  reflected 
ray,  c  a,  makes  with  the  same  perpendicular  ;  that 
is,  the  angle  d  c  b  is  equal  to  b  c  a,  or  the  angle  of 
incidence  is  equal  to  the  angle  of  reflection — the 

How  is  the  amplitude  determined  ?  What  is  the  height  and  what  the 
depth  of  the  wave  ?  What  is  a  ray  of  undulation  ?  What  law  do  waves 
observe  when  reflected  from  surfaces? 


216  NATURAL   PHILOSOPHr. 

same  law  which  is  observed  in  the  impact  of  solids  (page  78). 
As  the  same  law  applies  to  all  the  rays  which  constitute  the 
breadth  of  the  wave,  we  may  readily  determine  the  path  of  the 
reflected  wave  by  a  knowledge  of  the  form  of  the  surface  and  the 
angle  of  incidence. 

If  the  wave  is  linear,  that  is,  if  a  line  resting  upon  the  highest 
point  of  its  elevation,  at  right  angles  to  the  direction  in  which  it 
is  moving,  is  a  straight  line,  if  such  a  wave  meet  a  plane  surface, 
it  will  be  reflected  and  return  in  the  same  path.  If  it  meet  the 
surface  at  an  angle  of  20°  or  30°,  it  will  be  reflected  at  the  same 
angles  on  the  other  side  of  the  perpendiculars  to  the  reflecting 
surface. 

But  waves  are  generally  circular  or  curvilinear,  and  we  have 
to  consider  the  law  as  applied  to  the  reflection  of  such  waves 
from  surfaces  either  plane  or  curved. 

(1.)  If  the  wave  originate  from  the  center  of  a  cylindrical  ves- 
sel, the  rays  of  undulation  will  all  be  perpendicular  to  the  sur- 
face, and  will  return,  after  reflection,  to  the  center  in  exactly  the 
same  time. 

(2.)  If  the  vessel  is  in  the  form  of  an 
ellipse,  and  a  wave  originate  at  one  of  the 
focii,  all  the  rays  will  converge,  after  re- 
flection, to  the  other  focus ;  and  if  they 
proceed  from  the  focus  of  a  parabola,  a, 
Fig.  179,  they  will  be  reflected  in  paral- 
lel lines,  as  b  d,  e  d. 

(3.)  If  a  circular  wave  fall  upon  a  plane  surface  at  right  an- 
gles to  it,  then  the  different  rays  of  undulation  will  meet  the  sur- 
face in  successive  moments  of  time,  in  consequence  of  which  the 
form  of  the  reflected  wave  will  be  the  reverse  of  the  incident 
wave ;  that  is,  the  rays  which  first  strike  the  surface  will  be  re- 
flected first,  and  will  have  returned  to  the  same  distance  from 
the  surface  at  the  time  the  last  rays  meet  it,  that  these  last  rays 
were  at  the  moment  the  first  were  reflected. 

What  is  the  form  of  waves  ?  How  will  the  reflected  wave  move  if  it 
originate  at  the  center  of  a  circle  ?  How  if  it  originate  at  the  focus  of  an 
ellipse  ?  a  parabola  ?  If  a  circular  wave  fall  upon  a  plane  surface,  in  what 
manner  will  it  be  reflected  1 


INTERFERENCE    OF    WATER-WAVES. 


217 


'•  18°-  Thus,  suppose  the  wave  'g  a 

d,  proceeding  from  c,  Fig.  179, 
meet  the  plane  surface  ef.  The 
advance  portions,  as  at  a,  will 
first  be  reflected,  and  will  re- 
turn to  k  at  the  moment  that 
the  rays,  at  a  and  g  reach  the 
surface,  and  the  form  of  the 
wave  after  reflection  will  be  the 
same  that  it  would  have  been 
had  it  proceeded  from  c',  at  the 
same  distance  on  the  other  side 
ofef. 
3,  Interference  of  Water-Waves. — When  two  waves  on  the 

surface  of  a  liquid  encounter  each  other  under  certain  conditions, 

they  destroy  each  other's  effects,  and  are  then  said  to  interfere. 

This  interference  may  be  total  or  partial. 

Let  us  now  determine  the  conditions  under  which  total  and 

partial  interference  takes  place. 

Let  A  B,  Fig.  180,  be  the  surface  of  a  liquid,  A  g  the  length 

of  a  wave,  a  b,  c  f  the  intensity  or  amplitude  of  its  vibrations. 

Fig.  181. 


Let  a  second  wave  of  equal  length,  which  originated  half  a  wave's 
length  from  A,  and  is  moving  in  the  same  direction  with  equal 
intensity  of  vibration,  meet  it.  Then  this  second  wave  from  the 
point  d  will  move  in  the  direction  d  e  g,  exactly  opposite  to  the 
wave  afg.  All  the  individual  parts  of  each  wave  will  move  in 
opposite  directions  and  with  equal  velocity,  and  hence  they  must 
counteract  each  other's  motion,  and  a  total  interference  will  take 
place,  so  that  the  surface  will  remain  at  rest. 

(1.)  The  condition,  therefore,  under  ivhicfi  interference  is  pro- 
duced, is  when  the  elevation  of  one  wave  falls  into  the  depressions 
of  another,  and  this  will  always  occur  when  waves  of  equal 
lengths  have  come  through  paths  of  unequal  ivave  lengths. 


What  are  the  conditions  under  which  waves  interfere  with  each  other  ? 

K 


218 


NATURAL    PHILOSOPHY. 


If  the  spaces  through  which  the  second  wave  has  passed  are 
?>  l£>  2|  times  a  wave  length  of  the  first,  then,  when  they  meet, 
interference  will  be  total.  But  it  is  evident  that  waves  may 
originate  a  little  less  or  a  little  more  than  half  a  wave  length 
from  each  other ;  they  may  also  differ  in  intensity ;  in  which 
cases  only  partial  interference  will  take  place. 

Thus,  let  a  g  be  the  surface  of  the  wave  a  m  b  s  g,  Fig.  181, 
m  n,  q  s  the  intensity  of  its  oscillations,  and  let  another  wave  in- 

JF&.182. 


terfere  with  it  at  b,  having  the  intensity  q  r,  q  t.  As  this  second 
wave  is  moving  in  the  direction  q  r,  while  the  first  is  moving  in 
the  opposite  direction  q  s,  it  will  counteract  a  part  of  its  motion, 
and  the  intensity  of  the  vibrations  of  the  resulting  wave  will  be 
the  difference  between  q  s  and  q  r,  that  is,  q  t.  In  this  case  the 
interference  is  partial,  because  only  a  part  of  the  motion  of  the 
first  wave  is  destroyed. 

(2.)  If  two  systems  of  waves  of  equal  lengths,  which  have  pass- 
ed through  equal  spaces,  or  some  multiple  of  their  wave  lengths, 
encounter  each  other,  they  unite,  and  increase  the  intensity  of  the 
resulting  wave. 

Thus,  let  the  wave  a  m  p  b,  Fig.  183,  whose  intensity  of  vi- 
bration is  represented  by  m  n  and  o  p,  be  met  by  another  wave 

Fig.  183. 


at  b,  which  has  come  through  a  space  equal  to  once,  twice,  three 
times,  &c.,  the  wave  length  a  b;  then  the  elevations  and  de- 
pressions of  the  second  wave  will  coincide  with  those  of  the  first, 
and  increase  its  force. 

When  is  the  interference  of  waves  partial,  and  when  total  ?     When  do 
waves  increase  each  other's  effects  ? 


UNDULATIONS    OF    GASES.  219 

If  the  intensity  of  the  second  wave  is  equal,  q  r,  v  w,  then  the 
intensity  of  the  two  combined  will  be  represented  by  q  t,  v  x,  and 
the  resultant  wave  by  b  t  g  x  h.  If  the  waves  are  of  equal  inten- 
sity when  they  meet,  the  amplitude  of  the  resulting  wave  will 
be  doubled. 

Although  the  force  of  the  wind  is  supposed  not  to  extend  more 
than  20  feet  below  the  surface  of  the  water,  yet,  when  several 
systems  combine,  we  may  understand  how  they  may  accumulate 
upon  each  other,  and  produce  waves  of  much  greater  amplitude. 

4.  Standing  Waves. — It  is  evident  that  an  incident  and  re- 
flected wave  may  meet  under  such  conditions  as  to  produce  total 
interference,  that  is,  the  elevation  of  the  reflected  wave  may  fall 
into  the  depression  of  the  incident  wave,  so  that  a  line  resting 
on  the  surface  where  they  meet  will  be  at  rest.     This  will  form 
a  node  of  oscillation,  and  between  this  node  and  the  reflecting 
surface  there  will  be  formed  standing  waves. 

5.  Inflection  of  Waves,. — When  water  waves  fall  upon  a  soli^ 
surface,  through  which  at  any  point  there  is  an  opening,  as  whei* 
they  flow  through  a  short  channel  between  two  arms  of  the  sea, 

Fig.  184.  they  give  rise  to  several  systems  of  waves,  adja- 

cent to  the  opening,  which  interfere  with  each 
other  more  or  less  and  with  the  principal  wave. 
Thus,  suppose  a  wave  fall  upon  a  surface, 
and  pass  through  the  opening  a  b,  Fig.  183, 
it  will  give  rise  to  several  waves,  which,  by 
crossing  each  other,  produce  various  degrees 
of  interference.  This  phenomenon  is  called 
the  inflection  of  waves. 
IV.  Undulations  of  Gases.  Air-Waves.  —  Undulations  are 
produced  in  air  by  any  disturbance  of  its  density ;  and  though  air- 
waves, like  those  of  water,  have  a  progressive  motion,  they  differ 
from  water-waves  in  several  essential  particulars.  Air- waves  are 
formed  in  the  great  air  ocean  which  surrounds  the  earth,  and  not 
upon  its  surface. 

How  high  are  waves  formed  in  the  ocean  ?  How  are  standing  waves  and 
nodes  of  oscillation  produced  ?  What  is  meant  by  the  inflection  of  waves  ? 
By  what  means  are  waves  produced  in  the  air,  and  how  do  such  waves  dif- 
fer from  water-waves  ? 


220  NATURAL    PHILOSOPHY. 

Water-waves  are  due  to  gravity,  air-waves  to  elasticity.  In 
the  water-wave  the  separate  particles  rise  and  fall  at  right  an- 
gles to  the  direction  or  length  of  the  wave.  In  air-waves  the 
particles  move  back  arid  forth  in  a  line  with  the  advancing  wave, 
and  thus  produce  alternate  condensations  and  rarefactions  of  the 
separate  layers  of  air  which  make  up  the  length  of  the  wave. 

1 .  The  nature  and  laivs  of  air- waves  may  be  shown  by  means 
of  open  and  covered  pipes,  in  which  the  air  is  made  to  vibrate  by 

any  appropriate  cause. 

J?^.18& 

A          .  4  8  12  16  20  24  28  32 


II II 1 1 II I II 


A  4  B 

C  D 


4  8     12    16  20          24  28  32 

Let  A  B,  Fig.  185,  be  an  open  tube,  into  which  a  piston,  P, 
is  accurately  fitted,  so  that  vibrations  may  be  communicated  to 
the  air  within  it  by  a  rapid  motion  back  and  forth.  Let  the  air 
in  the  tube  be  divided  into  32  equal  layers.  Suppose  the  piston 
move  from.  A  to  8  and  back,  or  let  A  8  be  the  amplitude  of  its 
oscillations,  and  let  the  time  of  passing  from  1  to  8,  and  back 
again  to  1,  be  TVth  of  a  second,  the  piston  will  pass  from  1  to  2, 
&c.,  in  ^^th  of  a  second.  Each  layer  will  therefore  commence 
its  motion  -j  1  F^n  °^  a  secon(i  later  than  the  preceding. 

Such  a  piston,  however,  will  not  move  with  uniform  velocity, 
but  its  motion  will  be  greatest  midway  between  the  limits  of  its 
course,  or  at  4.  Hence,  when  it  passes  from  1  to  8,  the  air  will 
be  most  condensed  at  4,  and  when  it  returns  it  will  be  most  rar- 
efied at  the  same  point.  When  the  piston  has  passed  to  8,  or  the 
limits  of  its  course,  the  8th  layer  receives  the  impulse  and  com- 
municates it  toward  16,  and  wrhen  the  piston  has  returned  to  1, 
the  16th  layer  will  begin  its  motion.  The  condensed  part  of  the 
wave  will  be  at  1 2,  and  the  rarefied  portion  at  4  ;  and  when  the 
piston  commences  to  move  the  1st  layer  the  second  time,  the  16th 
layer  will  commence  its  motion.  This  determines  the  length  of  the 
wave.  That  is,  the  distance  between  two  layers  in  similar  states 
of  vibration  is  the  length  of  an  air-wave.  If,  therefore,  we  ex- 


UNDULATIONS    OF    AIR.  221 

amine  this  wave  after  one  vibration  of  the  piston,  we  shall  find 
that  it  consists  of  a  rarefied  and  condensed  portion,  the  greatest 
condensation  being  at  12,  and  the  greatest  rarefaction  at  4,  and 
that  the  layers  of  air  at  1  and  16  are  at  rest,  while  those  between 
1  and  8  are  moving  toward  1,  and  those  between  8  and  16  toward 
16.  The  condensed  portion  of  the  wave  corresponds  to  the  ele- 
vation, and  the  rarefied  portion  to  the  depression  of  a  water-wave. 
C  D  represents  the  wave  after  one  vibration. 

The  wave  will  not  stop,  however,  at  16,  but  will  be  propaga- 
ted to  32,  the  greatest  condensation  being  at  28,  and  the  greatest 
rarefaction  at  20  ;  and  at  the  same  moment  the  first  wave  will 
have  changed  its  position,  the  greatest  condensation  occurring  at 
4,  and  the  greatest  rarefaction  at  12. 

If  the  stroke  of  the  piston  is  repeated,  a  succession  of  waves 
will  be  formed.  Fig.  186  represents  the  condition  of  the  air  in. 

Fig.  186. 

321 


484440  36          322824-  20  l6  12    8  4 

the  tube  after  three  strokes  or  vibrations  of  the  piston,  and  the 
arrows  show  the  direction  in  which  the  separate  layers  are  moving. 

The  length  of  the  wave  depends  upon  the  time  the  piston  is 
making  an  oscillation.  The  slower  the  motion  the  longer  the 
wave,  and  the  more  rapid  the  motion  of  the  piston  the  shorter 
the  wave.  Thus,  if  the  time  occupied  by  the  piston  in  making 
an  oscillation  in  the  above  example  were  T\ ths  of  a  second  instead 
of  one,  the  wave  length  would  have  been  doubled,  and  if  it  had 
performed  an  oscillation  in  half  or  a  quarter,  &c.,  of  the  time,  the 
wave  length  would  have  been  but  half  or  a  quarter,  &c.,  as  long. 

The  intensity  of  the  wave,  however,  depends  upon  the  ampli- 
tude of  the  vibrations  of  the  piston,  because  the  air  becomes  more 
condensed  and  rarefied  as  the  amplitude  of  its  vibratory  particles 
is  increased.  It  will  make  no  difference,  however,  in  the  progress- 
ive motion  of  the  wave ;  the  shorter  waves  will  vibrate  so  much 

Of  what  does  an  air  wave  consist  ?     How  is  its  length  determined  ?    Upon 
what  does  the  length  of  the  wave  depend  ?     Upon  what  its  intensity  ? 


222  NATURAL    PHILOSOPHY. 

iaster  than  the  longer  that  they  will  each  traverse  a  given  space 
in  the  same  time.  Hence, 

Air-waves,  whatever  their  difference  of  length  or  intensity, 
are  propagated  with  the  same  velocity  and  rjass  over  equal  spaces 
in  equal  times. 

2.  Reflection  of  Air-Waves. — If,  instead  of  an  open  tube,  we 
take  one  which  is  covered,  that  is,  closed  at  one  end,  we  may  il- 
lustrate the  manner  in  which  air- waves  are  reflected,  the  relation 
which  the  length  of  the  tube  bears  to  the  length  of  the  wave,  and 
the  mutual  influence  of  the  incident  and  reflected  portion  of  a 
fvave  upon  the  character  of  its  vibrations. 

Let  the  tube  a  b,  Fig.  187,  which  is  closed  at  one  end,  be  a 

Fig.  187. 

a  be  d 


quarter  the  length  of  the  air- wave,  which  enters  it  at  its  open  ex- 
tremity. The  moment  that  the  layer  16  has  reached  the  bottom, 
where  it  will  be  thrown  back,  the  layer  12,  which  makes  one 
quarter  of  the  wave,  enters  it,  and  by  the  time  this  layer  would 
reach  the  bottom,  the  layer  8  would  enter  the  tube,  and  the  lay- 
er 16  would  have  returned  to  the  same  point ;  8  and  16  are  just 
half  a  wave  length  apart,  and  are,  therefore,  in  opposite  states  of 
density,  for  we  have  seen  that  the  distance  between  the  point  of 
greatest  condensation  and  the  greatest  rarefaction  is  just  half  a 
wave  length.  At  the  open  end  of  the  tube,  therefore,  the  great- 
est condensation  and  rarefaction  take  place  at  the  same  moment, 
and  destroy  each  other's  effects,  or  produce  total  interference; 
hence,  at  this  point,  the  layer  of  air  moves  backward  and  forward 
without  any  change  of  density.  'Shis  is  termed  a  belly.  All 
the  layers  of  air  in  the  tube  commence  their  motion,  reach  their 
limits,  and  commence  their  return  at  the  same  moment  of  time. 
The  layers  near  the  bottom  will  be  alternately  condensed  and 
rarefied,  while  those  near  the  open  extremity  will  not  be  changed 
in  density.  The  air  in  the  tube  is  thus  thrown  into  standing 
vibrations. 

What  law  governs  the  propagation  of  air-waves  ?     Illustrate  the  reflec- 
tion of  air-waves.     How  are  standing  vibrations  produced  7 


INTERFERENCE    OF    AIR-WAVES.  223 

3.  Interference  of  Air-Waves.     Nodes. — If  now  we  take  a 
tube,  a  d,  Fig.  188,  which  is  three  quarters  the  length  of  the 

Fig.  188. 

&•-*«    7i    *K»     C  d    **>    cf  <-s    n'  ci' 


air-wave,  and  divide  it  into  three  equal  parts  at  the  points  n  c, 
each  division,  as  a  n,  will  DC  one  quarter  of  the  length  of  the 
air-wave.  Suppose  the  wave  to  enter  the  tube,  and  pass  to  the 
bottom  to  d.  The  layers  of  the  wave  at  a  and  c,  which  are  re- 
moved one  half  the  length  of  the  wave  from  each  other,  are  in 
opposite  conditions  of  vibration.  When  the  layer  at  a  is  most 
condensed,  the  layer  at  c  is  most  rarefied,  and  the  reverse.  When 
the  wave  reaches  the  bottom,  it  is  reflected,  and,  on  its  return,  will 
reach  c  at  the  moment  that  the  layer  at  that  point,  which  is  half 
a  wave  length,  begins  to  move  toward  d;  and  as  the  two  layers 
are  in  opposite  states  of  vibration,  they  will  interfere,  and  pro- 
duce a  belly,  as  in  the  preceding  case. 

If  the  wave  had  proceeded  beyond  d  without  reflection,  there 
would  have  been  a  condensation  at  c'  and  a  rarefaction  at  a',  be- 
cause they  are  removed  half  a  wave  length  from  each  other ;  but, 
in  consequence  of  the  reflection  at  d,  c'  is  thrown  upon  c,  n'  upon 
n,  and  a'  upon  a.  At  the  point  n,  therefore,  there  will  be  a  con- 
densation, owing  to  the  meeting  of  the  advancing  and  returning 
wave ;  and  as  this  is  just  one  wave  length,  there  will  be  alternate 
condensations  and  rarefactions. 

If,  however,  we  examine  the  condition  of  the  layer  of  air  at  d, 
we  shall  find  that  it  is  at  rest,  being  acted  upon  by  equal  and 
opposite  forces,  produced  by  the  layers  of  air  moving  simultane- 
ously to  and  from  it ;  d,  then,  is  a  node  of  oscillation,  while  there 
will  be  bellies  at  a  and  c,  where  the  air  is  neither  condensed  nor 
rarefied,  but  merely  moves  back  and  forth. 

Under  these  conditions,  the  air  in  the  tube  is  thrown  into  stand- 
ing vibrations,  having  a  node  at  n  which  corresponds  to  the  nodes 
we  have  already  considered  in  the  undulations  of  solid  and  liquid 

Describe  the  manner  in  which  air- waves  interfere  and  produce  nodes. 


224 


NATURAL    PHILOSOPHY. 


bodies.  If  the  air-wave  is  much  shorter,  there  may  occur  two 
or  more  nodes  in  the  same  tube. 

Nodes  and  standing  vibrations  are  also  formed  in  open  tubes, 
provided  the  tube  bear  a  certain  relation  to  the  length  of  the  air- 
wave. The  reflection,  in  this  case,  takes  place  from  the  open  ex- 
tremities of  the  tube,  in  consequence  of  a  condensed  portion  of 
the  wave  arriving  at  these  points.  The  length  of  the  tube,  how- 
ever, bears  a  different  relation  to  the  wave. 

If  the  tube  is  one  half  the  length  of  the  wave,  there  will  oc- 
cur a  node  in  the  center  and  bellies  at  each  extremity.  This 
is  exemplified  in  Fig.  189,  A  B,  which  is  a  tube  half  the  length 

Fig.  189. 

ft   *" 


of  the  wave,  n  is  the  node,  and  the  layers  of  air  on  each  side 
simultaneously  move  to  and  from  this  point  toward  the  open  ex- 
tremities of  the  tube.  The  two  conditions  of  the  wave  are  rep- 
resented at  n  and  n'. 

If  the  open  tube  were  equal  in  length  to  the  air-wave,  then 
there  would  occur  two  nodes  at  n  and  n1,  Fig.  190  ;  and  if  the 

Fig.  190. 

L  <**  n         b  *»>  n  -*«M  s     n' n  TV    Y 


tube  were  two  thirds  the  length  of  the  wave,  then  there  would 
be  three  nodes,  one  in  the  center,  and  the  other  two  at  one  sixth 
of  the  length  of  the  tube.  The  formation  of  regular  air-waves 
in  closed  and  open  pipes,  and  the  occurrence  of  one  or  more 
nodes  of  oscillation,  give  rise,  as  we  shall  see,  to  different  tones, 
so  that  the  same  tube  will  emit  notes  of  different  pitch. 

We  have  considered  the  formation  of  regular  air-waves  in 
pipes,  but  waves  formed  in  the  air  are  precisely  similar  in  char- 
acter, and  observe  the  same  laws.  Air-waves  thus  excited  are 
similar  to  water-waves  in  form ;  that  is,  they  are  generally  cir- 

How  are  nodes  and  standing  vibrations  produced  in  open  tubes  ?  What 
is  the  relation  of  the  length  of  the  air-wave  tq  the  tube  in  order  to  produce 
one  or  more  nodes  ? 


ACOUSTICS.  225 

cular,  and  move  with  uniform  velocity.  Their  intensity  dimin- 
ishes as  the  square  of  the  distance,  and  the  extent  to  which  they 
may  be  propagated  is  only  limited  by  the  extent  of  the  atmos- 
phere. When  they  fall  upon  solid,  or  liquid,  or  even  gaseous 
bodies,  they  are  reflected,  according  to  the  same  laws  with  those 
of  water-waves.  If  a  ray  of  undulation  fall  perpendicularly,  it 
returns  by  the  same  path.  If  it  fall  upon  a  concave  surface,  its 
rays  are  collected  to  a  focus.  If  rays  proceed  from  one  focus  of 
an  ellipse,  they  are  reflected  to  the  other  focus.  The  further  con- 
sideration of  undulations,  however,  will  be  deferred  till  we  come 
to  treat  of  the  effects  of  undulations  upon  the  organs  of  sense, 
constituting  the  sensation  of  sound,  music,  light,  &c. 


CHAPTER  VI. 

ACOUSTICS. 

THE  term  Acoustics  is  derived  from  a  Greek  word,  which 
means  to  hear.  The  object  of  this  branch  of  Natural  Philosophy 
is  to  investigate  the  nature  and  laws  of  Sound.  As  sound  is  the 
effect  of  undulations  upon  the  organs  of  hearing,  we  propose  to 
consider,  1st.  The  subject  of  sound  in  general ;  and,  2d.  That  of 
musical  tones. 

SECTION  I.— OF  SOUND. 

Sound  is  a  sensation  produced  by  undulations  of  some  elastic 
medium  falling  upon  the  organs  of  hearing. 

I.  But  only  those  undulations  which  are  performed  within 
certain  limits  as  to  number  and  time  excite  the  sensation  of 
sound. 

II.  Sounds  are  various.     A  continued  sound  produced  by  the 
same  number  of  vibrations  per  second  is  called  a  tone. 

III.  Tones  are  high  or  low,  feeble  or  intense;  the  lowest  tone 
is  produced  by  16*5  vibrations  per  second,  and  the  highest  by 
about  16,000  vibrations  per  second. 

IV.  An  elastic  medium  is  necessary  to  conduct  sound.     Solids 


226  NATURAL    PHILOSOPHY. 

are  the  best  conductors,  liquids  rank  next,  and  gases  are  the 
poorest  conductors  of  sound. 

V.  Sounds,  whether  high  or  loiv,  feeble  or  intense,  are  conduct- 
ed in  the  same  medium  with  equal  velocity.     The  velocity  of 
sound  varies  in  solids,  but  is  much  greater  than  in  liquids  or 
gases.      Water  conducts  sound  4708  feet  per  second;  air  con- 
ducts it  at  the  rate  of  about  1120  feet  per  second. 

VI.  Sound  will  travel  to  a  great  distance  ;  furthest  in  solids, 
and  least  in  gases. 

VII.  When  sound  is  reflected,  it  gives  rise  to  echoes,  which  are 
single  or  multiple.      Upon  the  reflection  of  sound  and  its  concen- 
tration the  speaking  and  ear  trumpets  depend  for  their  utility. 

VIII.  Sound-waves  may  interfere  with  each  other  and  'pro- 
duce silence. 

SOUND  is  produced  ivhen  undulations  which  are  propagated 
through  some  material  medium  fall  upon  the  organs  of  hearing. 
Sound  is  a  sensation,  the  effect  of  undulations  in  an  elastic  body. 
The  origin  of  sound  is  therefore  the  same  as  that  of  undulations, 
which,  as  we  have  seen,  are  produced  by  the  disturbance  of  the 
particles  of  an  elastic  substance. 

The  medium  through  which  undulations  are  conveyed  to  the 
organs  of  sense  is  principally  the  air.  They  may,  however,  be 
communicated  through  solids  and  liquids,  or  they  may  originate 
in  solid  or  liquid  bodies,  be  communicated  to  the  air,  thence  to 
the  external  ear,  and  then  pass  again  through  solids  and  liquids 
to  the  auditory  nerve.  This  is  the  ordinary  mode  in  which  the 
sensation  of  sound  is  produced. 

We  have  considered  in  the  previous  chapter  the  origin  and 
laws  of  undulations  in  solids,  liquids,  and  gases.  It  remains 
now  to  point  out  their  relation  to  the  phenomena  of  sound ;  for, 
though  all  sounds  are  the  effect  of  undulations  upon  the  nerves 
of  sense,  yet  all  undulations  do  not  impress  these  organs  with 
the  sensation  of  sound. 

I.  Sound-waves  are  such  as  perform  their  vibrations  within 

How  is  sound  produced  ?  What  is  sound  1  What  connection  between 
undulations  and  sound  ?  Do  all  undulations  produce  the  sensation  of  sound  ? 
What,  then,  are  sound-waves? 


UNDULATIONS  PRODUCING  SOUND.          227 

certain  limits  as  to  time  and  number ;  that  is,  the  oscillations 
of  the  vibrating  wave  must  reach  a  definite  number  in  a  given 
time  in  order  to  excite  the  sensation  of  sound,  or,  if  they  exceed  a 
certain  number  in  a  given  time,  the  ear  will  not  be  impressed  by 
them,  or  will  not  be  able  to  distinguish  them.  These  limits 
must  be  determined  by  experiment.  They  are  found  to  vary 
slightly  when  judged  by  different  ears,  as  the  organs  of  hearing 
are  more  perfect  in  some  individuals  than  in  others ;  but,  except 
in  extraordinary  cases,  the  variation  is  too  slight  to  interfere  with 
general  laws. 

1 .  If  we  take  an  elastic  cord,  fixed  at  one  end,  and  stretch  it 
by  attaching  weights  to  the  other,  which  will  gradually  increase 
its  tension,  and  cause  it  to  vibrate  by  pulling  it  to  one  side,  we 
may  see  its  vibrations  until  the  increasing  tension  shall  cause 
16-5  to  be  made  in  one  second ;  then  the  intervals  entirely  dis- 
appear, and  at  the  same  moment  we  perceive  the  sensation  of 
sound.     It  is  found  that  the  vibrations  which  produce  the  im- 
pression are  from  16  to  17  per  second.     The  same  number  of  vi- 
brations per  second  will  be  impressed  upon  the  air-wave  which 
falls  upon  the  organs  of  sense  ;  hence  16 -5  vibrations  per  second 
in  a  vibrating  solid  or  fluid  are  the  lowest  number  which  the 
human  ear  can  perceive,  and  produce  the  lowest  tone  that  it  is 
capable  of  hearing. 

2.  If  now  the  number  of  vibrations  be  increased,  which  may 
be  done  by  shortening  the  string  or  increasing  its  tension,  or  both, 
the  tone  will  continue  to  rise  until  the  number  of  vibrations  has 
reached  16,000  per  second,  which  will  produce  the  highest  tone 
which  the  ear  can  discriminate.     If,  therefore,  the  vibrations  ex- 
ceed this  number,  human  ears  at  least  are  not  able  to  take  notice 
of  them,  or,  at  any  rate,  can  not  distinguish  the  tone  which  they 
may  produce. 

II.  Varieties  of  Sound. — The  impressions  made  upon  the  or- 
gans of  hearing  by  undulations  are  very  various,  and  have  re 
ceived  distinctive  names. 


How  many  vibrations  per  second  are  necessary  to  impress  the  organs 
of  sense  ?  What  is  the  effect  of  increasing  the  number  of  vibrations  ?  De- 
fine the  several  varieties  of  sound. 


228  NATURAL    PHILOSOPHY. 

When  an  elastic  body  is  struck  by  a  single  blow,  as  when  a 
bell  is  struck  by  its  tongue  or  an  explosion  produced  by  gun- 
powder/so  that  a  sudden  and  intense  air- wave  is  formed,  the 
sound  produced  is  called  a  report.  When  the  blow  is  repeated 
at  equal  intervals  of  time,  so  that  regular  and  equal  waves  are 
produced,  falling  upon  the  ear  so  rapidly  that  it  can  not  distin- 
guish the  intervals,  it  is  called  a  tone  ;  and  when  the  waves  of 
sound  are  of  unequal  lengths,  and  the  oscillations  are  repeated  in 
such  a  manner  as  to  interfere  with  each  other,  the  sound  pro- 
duced is  called  noise. 

III.  Varieties,  of  Tone. — Tones  are  distinguished  as  high  and 
low,  intense  and.  feeble. 

1.  The  lowest  tone  which  the  ear  can  discern  is  produced,  as 
we  have  seen,  by  a  wave  which  makes  16'5  vibrations  per  sec- 
ond ;  and  by  shortening  the  vibrating  body,  and  increasing  the 
number  of  vibrations,  the  tone  rises  higher  and  higher,  until 
16,000  vibrations  per  second  give  the  highest  tone.     Those  tones 
which  are  produced  by  the  slower  vibrations  are  low  tones,  and 
those  produced  by  the  more  rapid  vibrations  are  high  tones. 

2.  The!  intensity  of  the  tone  depends  upon  the  amplitude  of 
the  vibrating  particles,  and  not  upon  the  length  of  its  wave.     If, 
for  example,  a  stretched  cord  be  made  to  vibrate,  all  its  vibra- 
tions will  be  performed  in  the  same  time,  but  the  distance  through 
which  the  vibrating  parts  pass  on  each  side  of  their  line  of  rest 
may  vary.    If  this  distance  is  small,  it  will  produce  a.  feeble  tone; 
if  large,  a  loud  or  an  intense  tone. 

3.  The  quality  of  the  tone  is  not  so  easily  accounted  for.     The 
•same  tone  may  be  produced  by  a  violin,  a  trumpet,  or  the  human 
voice,  yet  the  tone  differs  very  much  in  quality.     It  has  been 
supposed  to  be  due  to  the  order  in  which  the  velocities  and 
changes  of  density  succeed  each  other  in  the  sound  waves  which 
produce  the  tone. — (Mutter.) 

IV.  Conduction  of  Sound. — We  have  seen  in  what  manner 
undulations  are  conducted  by  means  of  elastic  media ;  it  follows 

How  are  tones  distinguished  ?  Upon  what  does  the  intensity  of  the  tone 
depend  ?  What  gives  rise  to  the  quality  of  the  tone  ?  What  is  necessary 
in  order  to  conduct  sound  T 


CONDUCTION    OF    SOUND.  229 

that  sound,  using  the  term  not  only  for  jthe  sensation,  but  for  the 
undulations  which  produce  it,  must  have  some  elastic  medium 
for  its  conduction. 

1.  This  fact  may  be  readily  proved  by  experiment;  for  if  a 
body,  as  a  bell,  be  made  to  vibrate  in  a  vacuum,  no  sound  will  be 

perceived.     Thus, 

Exp. — Place  a  bell  on  some  cotton  wool  in  the 
receiver  of  an  air  pump,  Fig.  191,  and  cause  it  to 
be  rung  by  means  of  a  sliding  rod ;  its  vibrations 
will  be  communicated  to  the  air  in  the  receiver, 
and  from  thence  to  the  receiver,  which  will  pass 
them  on  through  the  external  air  to  the  ear,  and 
the  sound  will  be  distinctly  heard. 

Exp. — Let  the  air  now  be  exhausted,  and  the 
bell  rung  as  before ;  no  sound  will  be  heard,  be- 
cause there  is  no  medium  to  transmit  its  vibrations. 

Exp. — While  the  bell  is  vibrating,  admit  the  air 
slowly  to  the  receiver,  and  sound  will  begin  to  be 
heard,  at  first  feebly,  and  then  gr-owing  louder  as 
the  receiver  is  again  filled  with  air. 

Other  gases  and  vapors  will  also  transmit  the  vibrations  of 
sound  ;  for  if,  in  the  above  experiments,  a  few  drops  of  ether  or 
water  be  introduced,  after  the  air  is  exhausted  they  will  rise  up  in 
vapor,  and  the  sound  of  the  bell  will  be  distinctly  heard.  The 
experiment  may  be  varied  with  hydrogen  and  other  gases,  but  air 
is  one  of  the  best  conductors.  It  follows,  therefore,  that  no  sound 
can  be  communicated  beyond  the  limits  of  our  atmosphere,  be- 
cause there  is  nothing  to  continue  the  vibrations,  nor  can  any 
sounds,  however  loud,  reach  the  earth  from  any  of  the  planetary 
bodies.  The  intensity  of  sound  in  air  will  be  increased  by  con- 
densing it.  Thus,  if  a  bell  be  rung  in  a  receiver  of  condensed 
air,  .its  tone  will  be  much  more  intense ;  and  as  air  is  rarefied,  its 
power  is  diminished ;  hence,  on  high  mountains,  the  same  vibra- 
tions give  but  a  feeble  sound. 

2.  Liquids,  as  water,  are  good  conductors  of  sound.     This 
is  proved  by  the  fact  that  persons  under  water  are  enabled  to  hear 
sounds  which  have  originated  at  a  great  distance,  and  traveled 
through  the  intervening  water.     Water  is  a  better  conductor 
than  air. 

3.  Solid  bodies  are  still  better  conductors  of  sound  than  either 

How  is  this  proved  ?     What  bodies  conduct  sound  best? 


230  NATURAL    PHILOSOPHY. 

of  the  preceding  forms  of  matter.  This  may  be  shown  by  plac- 
ing the  ear  at  one  end  of  a  long  rod,  while  a  pin  is  drawn  across 
the  other  end.  A  slight  blow  on  the  end  of  a  solid  may  be  heard 
at  the  other  end,  though  it  may  be  several  times  the  distance  at 
which  the  same  sound  could  be  heard  in  the  air. 

Solids,  however,  differ  in  their  power  of  conduction.  Only 
those  which  are  elastic  are  capable  of  transmitting  sound-waves. 
Inelastic  bodies,  as  most  soft  bodies,  obstruct  the  vibrations,  and 
some  wholly  stop  them.  Glass,  the  metals,  wood,  and  stretched 
cords  are  among  the  most  elastic  bodies  which  conduct  sound. 
Very  porous  bodies,  as  wool,  obstruct  them.  India  rubber,  and 
some  other  elastic  substances,  are  destitute  of  conducting  power. 

V.  Velocity  of  Sound. — 1 .  The  velocity  of  sound  varies  in  dif- 
ferent media  ;  but  in  the  same  medium,  all  sounds,  whether  high 
or  low,  feeble  or  intense,  are  propagated  with  equal  velocity. 

This  law  results  directly  from  the  nature  of  undulations  pro- 
ducing sound.  The  length  of  each  wave  is  proportioned  to  the 
number  of  vibrations  in  a  given  time,  and  whether  the  tones  are 
feeble  or  intense,  high  or  low — whether  they  are  produced  by  a 
violin,  gunpowder,  or  the  human  voice,  the  undulations  which 
give  rise  to  them  traverse  a  given  space  in  the  same  time. 

This  law  is  also  proved  by  experiment  and  observation.  When 
we  listen  to  music  at  a  distance,  if  we  did  not  hear  the  high  and 
low,  the  feeble  and  intense  notes  at  the  same  moment,  there 
would  be  no  harmony,  and  we  should  hear  nothing  but  a  con- 
fused noise.  A  whisper  is  heard  at  the  same  moment  with  the 
loudest  tone.  There  is  a  great  difference  in  the  actual  distance 
at  which  a  feeble  and  an  intense  tone  may  be  heard,  but  no*  dif- 
ference in  the  velocity  with  which  they  are  propagated  in  the 
same  medium. 

2.  Sound  travels  ivith  different  velocities  in  different  media. 

(1.)  Solid  bodies  transmit  sound  with  different  degrees  of  ve- 
locity. This  is  due  to  their  elasticity  and  different  densities. 

It  has  been  found  by  experiment  that  sound  passes  in  a  bar  of 

Upon  what  property  does  the  conduction  of  sound  depend  ?  What  is  the 
velocity  of  sound  ?  How  is  its  velocity  ascertained  ?  Does  sound  travel  at 
the  same  rate  in  different  media  ? 


VELOCITY    OF    SOUND.  231 

tin  about  8400  feet  per  second,  in  a  copper  bar  13,440  feet,  and 
in  a  solid  tube  of  glass  19,040  feet  per  second.  It  passes  through 
other  solids  with  greater  or  less  rapidity.  This  velocity  is  de- 
termined by  noticing  the  time  required  for  vibrations  at  one  end 
of  a  bar  to  pass  and  be  heard  at  the  other  end. 

(2.)  Liquids,  as  water,  transmit  sound  with  much  less  veloc- 
ity than  solids.  According  to  the  experiments  of  Colladon  and 
Sturm,  which  were  made  on  the  waters  of  the  Lake  of  Geneva, 
the  velocity  of  sound  in  water  is  about  4708  feet  per  second. 
The  velocity  of  sound  in  water  is  determined  by  two  individuals 
placed  at  a  known  distance  from  each  other :  one  of  them  commu- 
nicates vibrations  to  the  water  by  striking  two  elastic  bodies  at  a 
given  instant,  and  the  other,  having  his  ear  in  contact  with  the  wa- 
ter, notes  the  exact  time  when  the  sound  is  heard.  The  distance 
divided  by  the  difference  of  time  in  seconds  will  give  the  velocity. 

(3.)  The  velocity  with  which  air  transmits  sound  has  also 
been  determined  by  experiment.  Though,  in  consequence  of  the 
fact  that  the  density,  temperature,  and  moisture  of  the  air  vary 
at  different  times,  there  is  a  slight  variation  in  the  rate  at  which 
sound  is  propagated  through  it,  yet  at  a  medium  pressure,  and  at 
a  temperature  of  60°  F.,  sound  travels  about  1120*  feet  per  sec- 
ond, or  about  one  fourth  as  rapidly  as  in  water,  and  only  about 
one  eighteenth  the  velocity  with  which  it  is  transmitted  in  glass. 
The  velocity  of  sound  in  air  is  determined  by  ascertaining  the 
time  required  for  it  to  pass  over  a  known  distance.  In  conse- 
quence of  the  almost  instant  passage  of  light  through  any  con- 
siderable distance  on  the  earth's  surface,  this  may  be  effected  by 
observing  the  flash  of  a  musket  at  a  certain  distance,  and  noting 
the  time  which  transpires  before  the  report  reaches  the  ear. 

*  The  velocity  of  sound  through  air  was  determined  in  France,  at  the  tem- 
perature of  32°  F.,  to  be  1086-1  feet  per  second.  Its  velocity,  as  determin- 
ed about  the  same  time  in  Holland,  was  1089-42  feet  per  second;  and,  as- 
suming that  its  velocity  is  increased  1-14  feet  per  second  for  an  increase  of 
one  degree  of  temperature,  the  velocity  at  a  temperature  of 62i°  F.  would 
be,  for  the  first,  1120-87,  and  for  the  second,  1124-19  feet  per  second; 
which  latter  is  the  rate  which  has  been  considered  most  correct.  Accord- 
ing to  this  rate,  sound  travels  12|  miles  per  minute,  or  765  miles  per  hour. 

Which  of  the  three  forms  of  matter  transmits  sound  with  the  greatest 
velocity  ?  How  is  the  velocity  of  sound  determined  ? 


232  N7ATURAL    PHILOSOPHY. 

If  the  air  is  moist,  the  velocity  is  slightly  increased.  A  wind 
in  the  same  direction  in  which  the  sound  travels  will  increase, 
and  in  the  opposite  direction  will  diminish  its  velocity. 

There  is  also  a  slight  variation  dependent  on  temperature. 
As  the  temperature  is  raised,  the  velocity  of  sound  is  increased 
about  one  foot  (1-14  feet)  for  every  degree.  Sound,  therefore, 
will  travel  faster  in  summer  than  in  winter,  faster  during  damp 
than  during  dry  weather. 

In  consequence  of  the  known  rate  at  which  sound  travels,  we 
may  determine  the  distance  at  which  any  report  is  made,  provid- 
ed we  are  able  to  observe  the  cause  of  it.  Thus  we  may  ob- 
serve the  blows  of  a  man's  ax  felling  a  tree  at  a  distance,  and 
by  noting  how  many  seconds  intervene  after  we  see  the  stroke 
before  the  sound  reaches  us,  the  exact  distance  may  be  known. 

In  this  case,  we  often  observe  the,  tree  to  fall  before  the  last 
stroke  reaches  the  ear.  The  distance  of  a  flash  of  lightning  may 
be  determined  in  the  same  way  by  counting  the  number  of  sec- 
onds which  intervene  between  the  flash  and  the  thunder.  The 
number  of  seconds  between  the  flash  and  the  report  of  a  cannon, 
multipled  by  1120  feet,  will  give  the  distance  it  is  from  us. 

VI.  Distance  to  which  Sound  may  be  propagated. — An  un- 
dulation communicated  to  the  air  or  any  elastic  medium  must 
travel  to  a  great  distance,  but  the  intensity  of  the  vibrations  must 
constantly  diminish.  If  the  vibrations  producing  sound  proceed 
from  a  center,  they  will  observe  the  same  law  with  any  other  in- 
fluence ;  their  intensity  will  be  inversely  as  the  square  of  the 
distance  ;  that  is,  at  four  times  the  distance,  the  sound  will  be 
but  one  quarter  as  loud ;  so  that,  though  we  may  not  be  able  to 
set  limits  to  the  undulations,  excepting  that  which  terminates 
the  medium,  still  they  will,  at  a  certain  distance,  become  too  fee- 
ble to  produce  the  sensation  of  sound. 

The  human  voice  is  said  to  be  heard  at  the  distance  of  700 
feet.  It  has,  however,  been  heard  at  a  much  greater  distance. 
From  Old  to  New,  Gibraltar,  a  distance  of  ten  miles,  the  watch- 
word "ALVs  Well!"  has  been  distinctly  heard. 

How  may  distances  be  determined  by  means  of  sound  1  To  what  dis- 
tance will  sound  reach  ?  What  law  governs  the  intensity  of  sound?  How 
far  can  a  man's  voice  be  heard  ? 


REFLECTION  OF  SOUND ECHO.  233 

The  report  of  a  musket  may  be  heard  about  four  miles,  and 
the  report  of  a  volcanic  eruption  has  been  heard  from  200  to  300 
miles  ;  in  the  latter  case,  however,  the  ground  aids  in  conducting 
the  sound. 

The  distance  to  which  sound  will  travel  is  influenced  by  the 
smoothness  or  roughness  of  the  surface  ;  it  may  be  heard  further 
across  water  than  on  the  land,  in  a  humid  than  in  a  dry  atmos- 
phere, further  in  the  night  than  in  the  daytime.  Water  trans- 
mits sound  further  than  air,  and  solids  further  than  liquids.* 

VII.  Reflection  of  Sound.  Echo. — 1 .  Air- waves,  as  we  have 
already  noticed,  when  they  fall  upon  different  surfaces,  are  reflect- 
ed, and  the  angle  of  incidence  is  always  equal  to  the  angle  of  re- 
flection. 

If  they  fall  perpendicularly  upon  a  smooth  surface,  they  will 
be  thrown  back  by  the  same  path. 

If  they  meet  the  surface  at  any  angle,  they  will  be  reflected  at 
the  same  angle  on  the  other  side  of  a  perpendicular  to  the  re- 
flecting surface. 

It  is  not  necessary,  however,  that  the  surface  should  be  smooth. 
Sound  is  reflected  from  the  sides  of  hills  and  rocks,  from  the  sur- 
face of  the  earth  and  of  water. 

Nor  is  it  necessary  that  it  should  fall  upon  a  solid  or  liquid 
body.  Sound  is  reflected  from  the  clouds,  and  even  from  the  clear 
atmosphere,  when  currents  of  air  of  different  densities  are  circu- 
lating. When  sound-waves-  are  reflected  from  any  surface,  they 
may  give  rise  to  what  is  termed 

2.  An  Echo. — If  the  sound  returns  to  the  point  from  whence 
it  originated,  it  must  meet  the  surface  at  right  angles,  and  in  this 
case  several  syllables  may  be  repeated.  By  a  rapid  utterance, 

*  Sounds  must  be  limited  by  the  media  in  which  they  are  propagated ; 
but  when  vibrations  are  once  given  to  the  air,  they  may  continue  long  after 
they  cease  to  affect  the  organs  of  sense ;  in  fact,  vibrations  in  air  may  con- 
tinue, for  aught  which  appears  to  the  contrary,  for  years,  so  that,  if  those 
organs  were  sufficiently  refined,  we  might  be  able  still  to  hear  the  voices 
of  friends  long  since  passed  away,  or  the  songs  of  other  days  and  of  former 
generations,  whose  vibrations  still  float  through  the  air. 

How  far  can  a  musket  be  heard  ?  What  influences  the  distance  ?  What 
media  transmit  sound  to  the  greatest  distance  ?  How  is  the  echo  produc- 
ed 1  Under  what  conditions  may  several  syllables  be  repeated  1 


234  NATURAL    PHILOSOPHY. 

eight  syllables  may  be  spoken  in  two  seconds.  If,  therefore,  we 
stand  at  the  distance  of  1120  feet  from  any  reflecting  surface}  we 
may  utter  eight  syllables,  and  they  will  be  returned  to  us.  If  the 
distance  is  increased,  the  number  may  reach  as  high  as  fifteen 
syllables,  which  may  be  distinctly  heard,  the  first  returning  at 
the  moment  the  last  is  uttered. 

3.  Multiple  Echoes. — It  is  evident  that  the  sound-wave  may 
be  reflected  several  times  if  it  fall  upon  surfaces  properly  situated. 
Such  echoes  are  known  to  exist  in  many  places,  particularly  in 
winding  valleys  which  lie  between  high  bluffs  or  rocks. 

There  is  a  valley  on  the  Rhine,  represented  in  Fig.  192,  in 

Fig.  192. 


which  the  sound  is  repeated  from  the  rocks  on  each  side  of  the 
river,  as  shown  at  1,  2,  3,  4. 

Near  Milan  there  is  a  place  where  the  sound  is  said  to  be  re- 
peated thirty  times. 

There  was  formerly  an  echo  at  Verdun,  where  the  sound  was 
reflected  from  the  surface  of  two  towers,  so  that  the  same  sound 
would  be  repeated  12  or  13  times. 

4.  Whispering  Galleries. — If  the  surface  from  which  sound- 
waves are  reflected  be  a  hollow  sphere,  and  the  waves  proceed 
from  its  center,  they  will  all  return  to  the  center. 

But  if  the  wave  fall  upon  a  concave  surface,  it  may  be  reflect- 
ed to  a  definite  point. 

Mention  examples  of  multiple  echoes.  How  are  whispering  galleries 
constructed  ? 


INTERFERENCE    OF    SOUND. 


235 


Fi    193 


Thus,  suppose  a  person  to  stand  at  the  point  gt  Fig.  193,  which 
is  the  focus  of  an  ellipse,  and  another 
at  c,  the  other  focus,  but  separated 
by  several  hundred  feet,  the  sounds 
which  proceed  from  each  focus  fall 
upon  the  surface,  as  gf,  c  e,  and  are 
reflected  to  the  opposite  focus. 
Persons  so  situated  may  converse  with  each  other  in  audible 
sounds  or  in  whispers,  and  be  distinctly  heard,  while  those  who  may 
occupy  the  intervening  space  are  unable  to  understand  a  single 
word.     Hence  such  structures  are  called  Whispering  Galleries. 
5.  Speaking  Trumpets. — It  is  on  the  principle  of  the  reflec- 
tion of  sound  that  speaking  trumpets  are  constructed.     In  these 
instruments  the  sound  is  reflected  from  the  sides  of  the  tube,  and 
the  intensity  of  the  vibrating  waves  is  greatly  augmented. 

Thus  the  waves, 
Figure  194,  are  pass- 
ed from  side  to  side 
through  the  tube,  and 
reflected  in  parallel 
lines,  so  that  nearly 
the  whole  force  of  the 
wave  is  projected  in  one  direction. 

With  a  tube  20  or  25  feet  in  length,  a  man  having  a  strong 
voice  will  make  himself  heard  two  or  three  miles. 
6.  Hearing  Trumpets. — The  hearing  trum- 
pet, Fig.  195,  is  similar  in  construction,  only  the 
sound-waves  enter  the  larger  end,  and  a  greater 
number  of  rays  are  collected  by  reflection,  and 
thrown  upon  the  organs  of  hearing. 
The  Stethoscope,  an  instrument  to  ascertain  the  condition  of 
the  organs  of  the  chest,  depends  upon  the  conduction  of  sound. 

VIII.  Interference  of  Sound. — We  have  shown  (page  223) 
that  air-waves  may  interfere  with  each  other  so  as  to  destroy 
their  effects ;  and  hence,  as  sounds  arise  from  such  waves,  there 
will  necessarily  occur  interference  of  sound. 

This  fact  may  be  shown  experimentally  by  passing  air-waves 
of  different  lengths  into  a  tube. 


Fig.  195. 


Describe  the  speaking  trumpet.    What  is  its  use  ?    Describe  the  hearing 
trumpet.     How  may  sounds  interfere  ? 


236 


NATURAL    PHILOSOPHY. 


Thus,  take  a  small  jar,  b,  Fig.  196,  and  by  means 
of  two  tuning  forks,  a  d,  of  the  same  note,  cause  it 
to  resound.  A  circular  card  must  first  be  placed  on 
one  prong  of  each,  and  a  drop  of  sealing-wax  on  one 
fork  to  increase  its  weight.  The  vessel  must  also 
be  filled  with  water  till  it  will  give  a  clear  note 
when  either  fork  is  held  over  its  open  extremity.  If 
now  both  forks  are  held  over  it  at  the  same  time, 
there  will  be  alternate  periods  of  silence  and  sound, 
produced  by  the  interference  of  the  longer  and  shorter  waves, 
which  meet  each  other  in  the  tube. 

Two  sounds  will  in  this  way  produce  silence*  This  phenom- 
enon is  not  confined  to  sound-waves  or  water-waves.  Two  rays 
of  light  may  produce  darkness,  and  two  rays  of  heat  cold,  as  will 
be  shown  more  fully  when  we  come  to  speak  of  the  interference 
of  light/ 

SECTION  II.— MUSICAL  TONES. 

HAVING  considered  the  manner  in  which  sound-waves  are  pro- 
duced and  propagated,  it  remains  now  to  investigate  the  relations 
which  exist  between  different  tones,  and  also  between  vibrations 
of  the  sounding  body  and  the  kind  of  tone  it  is  capable  of  yielding. 

There  are  certain  tones  or  combinations  of  tones  which  may 
succeed  each  other,  or  may  coexist  at  the  same  time,  and  produce 
an  agreeable  impression  on  the  ear,  and  hence  are  said  to  harmo- 
nize ;  and  when  the  vibrations  which  give  rise  to  them  are  per- 
formed in  equal  times,  to  be  in  unison.  There  are  other  tones 
which  strike  upon  the  ear  so  as  to  produce  a  disagreeable  sensa- 
tion, and  hence  they  are  said  to  be  unharmoni&us  or  discordant. 

When  several  tones  are  harmonious,  they  are  said  to  produce 
a  chord.  When  such  tones  succeed  each  other,  they  give  rise  to 
what  is  called  a  melody,  and  a  succession  of  chords  produces  what 
is  termed  a  harmony.  The  different  tones  are  called  notes,  or 
musical  notes. 

*  This  fact  may  explain  why  it  is  that  near  the  middle  of  a  large  hall  if 
is  often  difficult  to  hear  distinctly.  By  reflection,  the  sound-waves  from 
the  end  of  the  hall  interfere  with  those  which  proceed  from  the  speaker's 
voice,  and  destroy  their  effects. 

When  are  musical  tones  said  to  harmonize  ?  to  be  in  unison  ?  When  dis- 
cordant ?  What  is  a  chord  ?  harmony  ?  melody  ? 


VIBRATING   STRINGS    AND    MUSICAL    NOTES. 


237 


I.  Relation  betiveen  a  vibrating  String  and  musical  Notes. — 
Let  us  first  determine  the  relation  which  exists  between  a  vibra- 
ting cord  or  wire  and  musical  notes. 

For  this  purpose  the  sonometer  or  monochord  may  be  employ- 
ed. It  consists  of  a  hollow  box,  Fig.  1 97,  across  which  wires  or 

Fig.  197. 


'8 

i 

—  r 

Q 

*        $                =| 

HT              IT 

Q 

J 

g 

5" 


strings  may  be  stretched  by  means  of  weights,  P.  The  cord  is 
fastened  at  one  end,  C,  and  the  other  passes  over  a  pulley,  M,  and  is 
attached  to  the  weight  P.  Two  bridges,  F  F',  are  placed  near 
each  extremity.  There  is  also  a  movable  bridge,  H  H',  which 
may  be  placed  at  any  desirable  point,  so  as  to  shorten  the  string 
at  pleasure  by  pressing  it  upon  this  bridge  with  the  finger.  Such 
an  instrument  will  enable  us  to  ascertain  the  relation  between  the 
length,  weight,  and  tension  of  cords  and  musical  notes.  We  have 
seen,  page  207,  that 

1 .  The  number  of  vibrations  is  inversely  as  the  length  of  the 
string. 

2.  The  number  of  vibrations  is  as  the  square  root  of  its  tension, 
or  stretching  weight. 

3.  The  number  of  vibrations  of  strings  of  different  thickness 
is  inversely  as  their  diameters. 

1.  In  using  the  monochord  we  may  employ  one  string  at  a 
time,  and  vary  the  size  and  length  at  pleasure. 

Suppose  the  cord  C  M  be  gradually  stretched  by  the  weight 
P,  and  a  violin  bow  drawn  across  it.  As  long  as  the  eye  can 

Describe  the  sonometer.     Repeat  the  laws  of  vibrating  strings. 


238  NATURAL    PHILOSOPHY. 

trace  the  vibrations,  no  soimd  will  be  heard,  but  as  soon  as  its 
tension  enables  it  to  make  16*5  vibrations  per  second,  the  eye  fails 
to  perceive  any  intervals  between  them,  and  the  ear  is  impressed 
with  the  sensation  of  sound,  and  this  is  the  lowest  tone  which  it 
is  capable  of  discerning.  This  note  is  designated  by  Q.  The 
string  in  this  case  must  be  loaded  with  metal,  or  be  made  very 
long,  in  order  to  vibrate  with  sufficient  intensity  to  be  heard. 

2.  If,  now,  the  string  be  divided  in  the  center,  and  the  bow 
drawn  across  half  of  it,  it  will  perform  33  vibrations  per  second, 
and  the  note  is  called  an  octave,  and  designated  by  C.     If  but 
one  quarter  of  the  string  is  allowed  to  vibrate,  it  will  perform  66 
vibrations  per  second,  and  yield  a  note  which  is  a  second  octave, 
and  is  designated  by  C.     If  but  one  eighth  of  the  string  vibrate, 
it  will  perform  132  vibrations  per  second,  and  we  shall  have  a 
note  which  is  a  third  octave  of  C.    In  this  way  we  may  proceed 
dividing  the  string  until  we  reach  nine  octaves,  which  include 
the  whole  number  of  sounds  used  in  music.     There  is,  however,  a 
practical  difficulty  in  consequence  of  the  size  of  such  a  string,  and, 
in  order  to  obtain  the  higher  notes,  strings  of  less  diameter  and 
greater  tension  must  be  employed.     We  may  attach  a  weight  in 
the  above  case  four  times  that  which  gave  16*5  vibrations,  and 
obtain  the  octave,  or  33  vibrations,  and  then,  by  adding  four 
times  this  weight,  we  may  reach  the  second  octave,  or  66  vibra- 
tions per  second. 

3.  If  the  fundamental  or  lowest  note  which  a  string  with  a 
given  tension  will  make  be  represented  by  1,  then  the  lengths  of 
the  string  for  the  several  octaves  will  be  -£,  {th,  }th,  TVth,  &c.  ; 
or,  if  the  stretching  weight  be  represented  by  1 ,  the  added  weights 
for  the  octaves  will  be  4,  16,  64,  &c. 

But  there  are  eight  notes  in  each  octave,  which  are  designated 
by  the  letters  C,  D,  E,  F,  G,  A,  B,  C,  and  called  the  Diatonic 
Scale. 

How  many  vibrations  per  second  must  a  string  make  to  yield  the  lowest 
note,  or  C  ?  If  the  string  is  but  half  as  long,  how  many  vibrations  per  sec- 
ond will  it  perform  ?  How  are  the  octaves  produced  ?  How  must  the 
tension  be  increased  to  answer  the  same  purpose  as  halving  the  string? 
What  are  the  relative  lengths  of  strings  to  form  the  notes  of  the  diatonic 
scale? 


D.ATON.C    BCALB. 

The  length  of  string  necessary  to  produce  th 
represent  the  length  required  for  C  by  1,  will  be 
C        D        E        F        G        A        B 

1  I  I  *  I  i  T8 

As  the  number  of  vibrations  is  inversely  as  the  length  of  the 
string,  if  we  call  the  number  which  gives  C  1,  then,  by  invert- 
ing the  fractions  representing  the  lengths,  we  shall  be  able  to  ex- 
press the  relation  which  the  number  of  vibrations  of  each  note^n 
the  octave  bears  to  the  others.  Thus  : 

CDEFGABC 
1          £          f         t         I          I         ¥         2; 
and,  reducing  these  fractions  to  a  common  denominator,  we  have 
the  series 

CDEFGABC 
24        27        30        32        36        40        45        48. 

The  string  which  gives  the  note  C  makes  24  vibrations,  while 
that  which  yields  the  note  D  makes  27,  E  30,  F  32,  &c. 

Now  chords  will  occur  whenever  the  vibrations  of  the  several 
strings  bear  a  definite  relation  to  each  other,  or  when  their  vibra- 
tions frequently  coincide.  Thus  C  makes  4  vibrations  while  E 
makes  5,  C  makes  3  while  F  makes  4,  C  makes  2  while  G  makes 
3  ;  and  as  the  vibrations  in  this  last  note  more  frequently  coin- 
cide with  C,  it  is  a  more  perfect  chord  ;  it  is  called  a  fifth,  being 
the  fifth  note  from  C.  If  we  examine  the  intervals  between  the 
notes,  we  shall  find  that  they  are  not  all  equal.  Thus  the  in- 
terval between  24  and  27  is  jth,  between  27  and  30  £th,  &c., 
giving  the  series  for  the  intervals  between 

CDEFGABC 

I  *  TV  *  *  I  iV 

That  is,  there  are  three  intervals  of  |th  and  two  of  £th.  The 
former  are  called  full  perfect  tones,  and  the  latter  small  perfect 
tones.  The  two  intervals  between  E  F  and  B  C  are  each  yjth, 
and,  as  they  are  nearly  half  as  great  as  those  between  the  oth- 
er notes,  they  are  called  semitones  or  hemitones. 

How  may  the  relative  number  of  vibrations  for  each  note  of  the  scale  be 
expressed  ?  When  will  the  more  perfect  chords  be  produced  ?  Are  the 
intervals  equal  ?  What  are  full  tones,  and  what  semitones  ? 


240  NATURAL    PHILOSOrii  *  . 

4.  By  shortening  the  string,  diminishing  its  diameter,  or  in- 
creasing its  tension,  we  might  pass  in  the  same  manner  through 
the  several  octaves,  but  it  would  be  a  repetition  of  a  similar  series, 
and  we  should  find  that  though  every  eighth  note  from  C  would 
form  a  perfect  chord  with  the  lowest  note  which  the  string  might 
give,  yet  the  octaves  of  some  of  the  other  notes  would  cause  a 
slight  discord.     Thus,  while  the  key  note  C  makes  one  vibra- 
tion, E,  which  is  called  the  major  third  of  C,  makes  f  vibrations, 
and  the  major  third  of  this  note  is  £  of  £ ,  or  f  f  vibrations,  and 
the  major  third  of  this  last  note  is  f  of  f  of  f ,  or  ^V  vibrations. 
This  third  note  does  not  exactly  accord  with  the  octave  of  the 
fundamental  note,  which  is  represented  by  y¥8 .     When  we  as- 
cend, then,  through  full  thirds,  we  fall  below  a  pure  octave.     The 
same  is  true  of  the  fifths,  which  rise  above  the  pure  octave  of  the 
key  note,  and  hence  musicians  cause  these  notes  to  be  raised  or 
lowered  a  little  to  preserve  the  purity  of  the  octaves.     This  is 
called  temperament. 

5.  Intermediate  notes  are  often  wanted  between  those  whose 
interval  is  a  perfect  tone.     These  notes  take  their  name  from  the 
note  above  or  below  them,  and  are  called  sharped  or  flatted  notes. 
Thus,  the  note  between  C  and  D  is  called  sometimes  C  sharp,  and 
sometimes  D  flat,  according  to  circumstances.    Between  E  and  F, 
and  between  B  and  C,  there  can  be  no  flatted  or  sharped  note. 

6.  In  the  piano-forte  the  strings  are  of  different  lengths,  differ- 
ent diameters,  and  some  of  them  loaded ^with  metal  in  order  to 
yield  the  lower  notes,  the  same  string  yielding  but  one  tone. 

In  the  viol,  tenor  or  bass,  the  tones  are  modified  by  the  size 
and  different  degrees  of  tension  given  to  the  string,  and  the  same 
string  is  made  to  yield  several  notes  by  shortening  it  with  the  fin- 
gers. In  such  instruments,  all  the  strings  being  of  the  same 
length,  those  which  yield  the  lower  notes  are  also  loaded  with 
metal,  to  diminish  the  rapidity  of  vibration. 

In  the  harp  the  strings  are  varied  in  size,  length,  and  tension 
II.  Musical  Tones  in  Pipes. — Having  considered  the  relation 

How  may  several  octaves  be  attained  by  strings  ?  Under  what  condi- 
tions will  the  octaves  form  chords  ?  discords  ?  What  are  flats  and  sharps, 
and  what  is  their  use  1  How  are  the  different  notes  produced  in  the  piano- 
forte ?  in  the  viol  ?  the  harp  ? 


MUSICAL    TONES    OF    PIPES.  241 

between  stretched  strings  and  the  tones  which  they  are  capable 
of  yielding,  we  proceed  now  to  investigate  the  relations  existing 
between  air-waves  and  these  same  musical  notes,  for  it  is  through 
the  medium  of  air-waves  that  the  vibrations  of  strings  convey 
their  impressions  to  the  ear.  We  have  seen  that  when  air  is 
made  to  vibrate  in  a  covered  or  open  pipe,  the  vibrations  consist 
of  successive  condensations  and  rarefactions  of  the  layers  of  air, 
the  motion  taking  place  in  the  direction  of  the  length  of  the  tube. 
]Let  us  now  ascertain  the  length  of  the  air-waves  necessary  to 
produce  given  tones  in  connection  with  open  and  covered  pipes. 
1.  Covered  Pipes. — If  we  take  a  covered  pipe,  a  b,  Fig.  198, 

Fig.  198. 

a  be  d 


16  feet  in  length,  and  cause  it  to  resound  by  bringing  a  vibra- 
ting string  or  plate,  which  makes  16 '5  vibrations  per  second,  near 
its  open  end,  it  will  yield  the  lowest  note,  Q,  or  the  sound-wave 
which  is  formed  will  make  16-5  vibrations  per  second.  Now 
we  have  seen  that,  in  order  that  the  air  in  such  a  pipe  may  be 
thrown  into  regular  vibrations,  the  tube  must  be  ^th,  f  ths,  f  ths, 
^ths,  &c.,  the  length  of  the  wave.  The  lowest  note,  therefore, 
which  a  covered  pipe  will  yield  must  have  an  air- wave  four  times 
its  length.  The  air-wave,  then,  which  yields  the  lowest  tone,  C, 
must  be  64  feet  in  length. 

The  length  of  this  wave,  which  gives  the  lowest  note,  may  be 
confirmed  by  the  rate  at  which  sound  travels.  If  we  assume 
that  the  velocity  of  sound  is  1120  feet  per  second,  then  a  wave 
64  feet  in  length  would  traverse  a  tube  16  feet  in  length  17'5 
times  in  a  second  ;  but  the  velocity  of  sound  varies  with  the  tem- 
perature. If  we  assume  that  the  medium  velocity  of  sound  is 
1056  feet  per  second,  then  a  wave  64  feet  in  length  would  trav- 
erse a  tube  16  feet  long  16-5  times  per  second  :  16'5  X  64  —  1056. 

A  covered  pipe,  then,  16  feet  long,  will  yield  the  lowest  note, 

How  are  musical  tones  produced  in  pipes  ?  What  is  the  length  of  an 
air-wave  which  yields  the  lowest  note  ?  How  is  its  length  determined  ? 
In  what  other  manner  is  the  length  of  the  wave  which  yields  the  lowest 
note  ascertained  ? 

L 


242  NATURAL    PHILOSOPHY. 

and  its  wave  length  is  64  feet.  This  same  pipe  may  yield  other 
notes.  The  next  higher  note  will  have  a  wave  length  fds  the 
length  of  the  pipe,  and  the  third  note  will  have  a  wave  length 
f  ths  the  length  of  the  pipe.  The  higher  notes  are  produced  by 
the  formation  of  nodes  of  oscillation  in  the  pipe,  just  as  a  string 
may  give  a  higher  note  by  dividing  itself  into  parts,  with  nodes 
forming  standing  vibrations.  If  we  diminish  the  length  of  the 
pipe,  the  key  note  will  be  raised. 

A  covered  pipe  4  feet  long,  which  has  a  wave  length  of  16  feet, 
will  yield  the  note  C  of  the  diatonic  scale.  Now  the  no.tes  which 
combine  with  C,  and  make  an  agreeable  impression  upon  the  ear, 
are  produced  by  air- waves  whose  lengths  are  |,  fds,  |ths,  f  ths, 
f  ths  of  the  length  of  the  wave  which  yields  C,  and  hence  these 
notes  may  be  produced  by  pipes  which  are  |,  fds,  &c.,  the  length 
of  the  pipe  C.  The  time  of  oscillation  is  inversely  as  the  wave 
lengths,  so  that  these  fractions  inverted  will  express  the  relation 
between  the  number  of  vibrations  of  'he  several  air-waves  ;  and 
hence,  while  C  makes  1  vibration,  the  next  note,  f.,  will  make  2. 
This  note  is  the  octave  of  C.  The  next  note,  whose  wave  length 
is  |ds  of  C,  will  make  3  vibrations  while  C  makes  2,  and  tin's  is 
called  the  5th  of  C,  and  is  designated  by  G. 

The  next  note,  f  ths  the  wave  length  of  C,  makes  4  vibrations 
while  C  makes  3,  and  is  the  4th  of  C,  and  designated  by  F.  The 
note  having  a  wave  length  £ths  of  C,  makes  5  vibrations  to  4  of  C, 
and  is  the  major  third  of  C,  designated  by  E  ;  and  the  note  whose 
wave  length  is  |ths  of  C,  makes  6  vibrations  while  C  makes  5. 
This  is  the  minor  third  of  C,  and  marked  E  flat.  We  have, 
then,  the  following  series  of  notes,  making  vibrations  simultane- 
ously, according  to  the  numbers  : 

C        E        F        G        C 
24       30        32        36        48. 

In  order  to  complete  the  scale,  E,  F,  and  G  must  have  their 
octaves,  thirds,  and  fifths.  The  fifth  of  G  makes  3  vibrations 
while  G  makes  2,  and  the  next  lower  octave  of  this  note  makes 

Will  the  same  pipe  yield  other  notes  ?  What  note  will  a  covered  pipe 
four  feet  long  give  ?  How  are  the  wave  lengths  of  the  several  notes  of  the 
scale  determined  ?  Describe  the  manner  in  which  the  several  notes  of  the 
pcale  are  found,  and  the  letters  which  designate  them. 


ORGAN    PIPES.  243 

27  vibrations  to  36  of  G  and  24  of  C.  This  is  D.  The  major  third 
of  G  is  B,  which  has  5  vibrations  to  4  of  G,  or  45  of  B  to  36  of  G. 
The  fifth  of  F  makes  48  vibrations  while  F  makes  32.  This  is 
the  octave  of  C  ;  and  the  major  third  of  F  makes  40  vibrations  to 
32  of  F,  and  is  designated  by  A.  We  have,  then,  the  following 
series  of  notes,  called  the  C  gamut,  whose  simultaneous  vibrations 
are 

CDEFGABC 
24        27        30        32        36        40        45        48; 

and  the  wave  lengths  of  these  notes,  representing  the  wave  length 
of  C  by  1  ,  are, 

CDEFGABC 


I       I 


which  shows  the  same  relations  as  exist  between  the  length  of 

cords  and  the  notes  which  are  yielded  by  them. 

Fig.  199-  It  is  obvious  that  a  series  of  pipes  corresponding  with  the 
length  of  the  air-waves  above  considered  may  be  arranged 
so  as  to  constitute  a  musical  instrument. 

Organ  pipes  are  arranged  in  accordance  with  these 
laws.  The  pipe,  Fig.  199,  consists  of  a  pedal,  P,  which 
has  a  slit  in  it  to  admit  the  air  from  the  bellows,  and  a 
tube  with  a  mouth-piece,  t.  The  air  in  the  tube  is  thrown 
into  vibrations  by  that  which  passes  through  the  pedal, 
and  strikes  against  the  upper  lip  of  the  mouth-piece.  The 
organ  pipe  is  similar  to  a  ^vh^stle. 

In  flutes  and  similar  ivind  instruments,  the  several 
notes  are  produced  by  apertures  placed  so  as  to  produce 
the  same  effect  as  shortening  the  tube  ;  and  hence,  in  this 
t  case,  the  tube,  and  consequently  the  air-  waves,  are  length- 
ened or  shortened  by  means  of  the  fingers  and  keys,  by 
which  the  apertures  may  be  opened  and  closed  at  pleasure. 
2.  Open  Pipes.  —  Air-  waves  formed  in  open  tubes  may 

form  a  series  of  musical  notes,  provided  the  tubes  bear  a  certain 

relation  to  the  length  of  the  waves.     But  in  consequence  of  the 

How  are  the  wave  lengths  represented,  and  what  relation  do  they  bear 
to  the  wave  length  of  the  key  note,  or  C  ?  Describe  the  organ  pipe.  How 
are  notes  formed  in  flutes  and  similar  wind  instruments? 


NATUPtAL    PHILOSOPHY. 


fact  that  the  wave  is  not  reflected  at  the  bottom  of  the  tuhe,  but 
at  the  open  extremities,  the  pipe,  to  produce  the  lowest  note,  C, 
must  be  32  feet  long,  as  the  wave,  which  is  64  feet,  will  not  be 
reflected  until  half  of  it  has  entered  the  pipe.  In  this  case  there 
will  be  a  node  of  oscillation  in  its  center,  Fig.  200,  and  the  three 


Jl 


Fig.  200. 

B     C 


notes  which  such  a  pipe  will  give  will  have  air- waves  whose 
lengths  are  twice  the  length  of  the  tube,  once  its  length,  and 
once  and  a  half  its  length  ;  in  the  second  note  there  are  two  nodes 
of  oscillation,  and  in  the  third  three  nodes,  Fig.  20 1 .  The  same 

Fig.  201. 

L  «*•*  n         b  a»>  n  ««KM  s     nf n,  TV    Y 


relation  exists  between  the  air- waves  and  the  length  of  a  tube, 
whatever  its  key  note  may  be. 

3.  Reed  Pipes. — In  reed  pipes  a  tongue  is  the  vi-  Fig.  202. 
brating  body,  which  is  set  in  motion  by  a  current  of 
air,  and  communicates  its  vibrations  to  the  air  in  the 
pipe.  The  tongue  consists  of  a  flat  piece  of  metal  or 
elastic  wood,  r,  Fig.  202,  placed  over  a  slit  in  the 
mouth-piece  or  hollow  tube,  c,  and  fastened  at  one  end. 
A  tuning  wire,  t,  is  made  to  slide  up  and  down,  so  as 
to  shorten  or  lengthen  the  tongue.  In  its  vibrations 
it  observes  the  laws  of  vibrating  rods.  In  some  forms 
the  wind  enters  c  through  a  pedal  and  bellows  attach- 
ed to  it,  and  in  others  it  is  forced  in  through  the  mouth. 

III.  Transmission  of  Tones. — We  have  seen  that 
sound-waves  may  be  transmitted  from  solids  and  liquids  to  air, 
and  the  reverse ;  but,  in  passing  from  one  medium  to  another, 
the  sound  is  partially  or  wholly  impeded. 

Thus  the  vibration  of  a  tuning  fork  emits  but  a  faint  sound ; 
but  the  vibrations  may  be  more  readily  communicated  to  the  air 
by  causing  it  to  vibrate  in  contact  with  a  larger  vibrating  sur- 

What  relation  between  the  wave  lengths  of  notes  and  the  length  of  open 
pipes  ?  What  is  the  vibrating  body  in  reed  pipes?  Describe  the  tongue. 
How  may  sounds  be  transmitted  from  one  medium  to  another! 


ORGANS    OF    VOICE.  245 

face,  as  a  hollow  box.  A  musical  box  will  in  this  way  transmit 
its  vibrations  to  the  air  with  more  intensity  if  placed  on  some 
body,  as  the  cover  of  a  piano,  to  increase  the  vibrating  surface. 

Air-waves  falling  on  solid  or  liquid  bodies  are  also  impeded 
unless  their  length  correspond  with  the  length  of  the  wave  which 
the  solid  is  capable  of  yielding. 

fig-  203.  Thus,  if  a  string, 

h  as  e  d,  Figure  203, 

stitched,  and  a 
bridge,  b,  placed  at 
about  one  third  of 
its  length,  and  a  bow  be  drawn  across  at  a,  the  part  b  d  will  be 
thrown  into  vibrations,  dividing  itself  into  two  parts,  with  a  node 
at  n  yielding  the  same  tone  as  e  b.  This  is  sometimes  called 
the  Sympathy  of  Sounds. 

The  JEolian  Harp  produces  its  various  notes  by  dividing  it- 
self so  as  to  be  in  sympathy  with  the  varying  force  of  the  wind. 

We  may  notice  the  effect  of  an  organ  in  a  church.  At  the 
recurrence  of  certain  notes,  the  pillars  and  whole  building  are 
shaken  with  vibrations. 

A  speaker,  the  key  note  of  whose  voice  corresponds  to  that  of 
the  room,  will  speak  with  much  greater  ease,  as  the  vibrations 
of  the  room  aid  his  voice. 

When  certain  notes  are  struck  on  a  piano-forte,  the  lamps  or 
crockery  in  the  room  will  often  vibrate.  It  is  said  that  some 
musicians  have  the  power  of  throwing  a  glass  or  china  vessel  into 
such  violent  vibrations,  by  sounding  its  key  note,  as  to  break  it 
into  many  pieces. 

IV.  Organs  of  Voice. — The  windpipe,  through  which  air  en- 
ters the  lungs,  is  a  tube  made  up  of  rings  of  cartilage,  and  termin- 
ated at  its  upper  extremity  by  what  is  called  the  larynx,  which 
constitutes  the  organ  by  which  different  tones  are  produced.  Ar- 
ticulate sounds  constituting  speech  are  made  principally  by  means 
of  the  tongue,  palate,  and  lips,  in  connection  with  the  action  of 
the  larynx. 

What  is  meant  by  sympathy  of  sounds  ?  When  will  the  pillars  of  a 
church  vibrate?  What  effect  upon  bodies  to  sound  their  key  note  near 
them  ?  By  what  organs  are  different  tones  produced  ?  What  organs  are 
concerned  in  articulate  sounds? 


246 


NATURAL    PHILOSOPHY. 


204-  The  larynx  consists  of  four  cartila- 

ges :  a,  Fig.  204,  is  called  the  cricoid 
cartilage,  and  surrounds  the  base  of  the 
larynx ;  b  b  is  called  the  thyroid  carti- 
lage; c  c,  the  two  arytenoid  cartilages; 
d  is  the  epiglottis,  which  lies  above  the 
glottis,  e.  The  edges  of  the  glottis  con- 
sist of  very  elastic  tissue,  forming  what 
is  called  the  chordce  vocales,  v,  which 
may  be  more  or  less  stretched  by  appro- 
priate muscles.  The  formation  of  notes 
is  similar  to  reed  pipes,  the  vibrations 
being  performed  by  the  chordae  vocales, 
which,  with  the  action  of  the  other  mem- 
branes, open  and  close  the  glottis  with  great  rapidity,  allowing 
the  air  to  escape,  and  throwing  it  into  vibrations,  which  yield 
tones  high  or  low,  intense  or  feeble,  according  to  the  tension  of 
the  vibrating  tissues  and  force  of  the  air  from  the  lungs.  For  a 
full  description  of  the  organs  of  voice  and  of  hearing,  the  student 
is  referred  to  works  which  treat  more  at  length  of  these  organs. 

V.  Organs  of  Hearing. — The  organs  of  hearing  consist  of 
three  main  parts  :  the  external  ear,  the  cavity  of  the  tympanum, 
which  is  separated  from  the  external  ear  by  a  membrane,  and 
the  labyrinth.  The  external  ear  consists  of  the  pinna,  C,  and 
the  meatus,  M,  Fig.  205,  which  convey  the  waves  of  sound  to 

Fig.  205. 


Describe  the  larynx.     What  are  the  principal  parts  concerned  in  speak- 
j  ?    Of  what  do  the  organs  of  hearing  consist  ? 


CALORIC.  247 

the  membrane  of  the  tympanum,  D,  which  has  attached  to  it 
on  the  inner  side  a  small  bone  called  the  malleus,  B,  which  is 
also  connected  with  three  other  bones ;  the  second  is  called  the 
incus,  the  third  os  orbiculare,  and  the  fourth  stapes,  T,  which 
closes  the  funestra  ovalis.  The  tympanum  cavity,  V,  is  con- 
nected with  the  Eustachian  tube,  E,  opening  into  the  mouth, 
and  the  air  in  the  labyrinth,  K  S,  is  put  into  vibrations  by  the 
vibrating  bones,  and  communicates  with  the  auditory  nerve,  N, 
where  the  sensation  is  conveyed  to  the  mind.  The  use  of  the 
bones  is  not  only  to  conduct  the  vibration,  but  to  increase  the 
tension  of  the  membrane  of  the  tympanum,  so  as  to  modify  the 
intensity  of  the  sound. 


CHAPTER  VII. 

OF  CALORIC  OR  HEAT. 

Heat  or  caloric  exists  in  two  states,  Sensible  and  Insensible. 

I.  Sensible  caloric  lias  one  general  property,  which  is  a  tenden- 
cy to  diffuse  itself  equally  among  the  atoms  of  matter,  and  to 
form  an  equilibrium  of  temperature.      This  is  effected  by  con- 
duction and  radiation. 

II.  Sensible  caloric  has  one  principal  effect,  which  is  a  tenden- 
cy to  expand  all  bodies,  solid,  liquid,  and  gaseous. 

III.  Insensible  caloric  gives  rise  to  the  liquid  and  gaseous 
forms  of  matter,  and  produces  the  phenomena  of  liquefaction 
and  vaporization  ;  hence, 

IV;  By  heating  water  it  may  be  converted  into  steam,  which, 
in  connection  with  the  steam-engine,  is  employed  as  a  most  use- 
ful and  efficient  mechanical  power. 

THE  subject  of  caloric  belongs  to  Chemistry,  but,  as  heat  is  a 
powerful  mechanical  agent,  there  is  one  branch  of  it  which  comes 
appropriately  under  the  notice  of  the  natural  philosopher. 

Caloric  exists  in  two  states  :   1 .  Sensible,  in  which  state  it  pro- 
Describe  the  several  parts  of  this  organ.     Where  is  the  sound  perceived? 
To  what  science  is  caloric  assigned  ?     In  how  many  states  does  it  exist  ? 


248  NATURAL    PHILOSOPHY. 

duces  the  sensation  of  heat,  and  tends  to  expand  all  bodies  into 
which  it  is  introduced. 

2.  Insensible,  in  which  condition  it  does  not  affect  the  temper- 
ature of  bodies,  but  exists  in  them  in  greater  or  less  quantities, 
and  gives  rise  to  the  liquid  and  gaseous  forms  of  matter. 

I.  Sensible  Caloric  has  one  fundamental  property,  which  is  a 
tendency  to  diffuse  itself  equally  through  all  bodies;  that  is, 
to  bring  all  bodies  to  an  equilibrium  of  temperature.  This  is 
effected  in  two  ways  : 

1 .  By  conduction,  in  which  case  it  passes  from  particle  to  par- 
ticle through  any  body.     The  rapidity  with  which  it  passes  va- 
ries greatly  in  different  substances.     Solids  are  almost  the  only 
bodies  which  conduct  heat  at  all.     In  liquids  the  power  is  very 
slight.     In  gases  it  is  wholly  wanting. 

Solids  are  heated  by  conduction,  but  liquids  and  gases  are  heat- 
ed by  convection,  that  is,  by  contact  of  their  particles  against 
the  surface  of  some  heated  solid. 

2.  By  radiation,  in  which  case  caloric  is  thrown  off  in  all  di- 
rections from  the  surface  of  a  heated  body  in  right  lines,  and  pass- 
es through  air  and  other  gases  without  heating  them. 

When  radiant  caloric  falls  upon  solid  or  liquid  surfaces,  it  is 
either  reflected,  that  is,  thrown  back  from  the  surface  in  the  same 
manner  as  a  solid  would  be ;  or  it  is  absorbed,  that  is,  passes  into 
the  body  and  heats  it ;  or  transmitted,  that  is,  passed  directly 
through  the  body.^ 

II.  Sensible  Caloric  produces  one  generic  effect,  Expansion. 
It  expands  all  bodies,  solids,  liquids,  and  gases.  In  solids  and 
liquids,  the  degree  of  expansion  varies  in  different  substances,  and 
in  the  same  substance  at  different  temperatures ;  but  all  gases  are 
equally  expanded  by  heat,  whatever  their  temperature  may  be ; 
that  is,  equal  additions  of  caloric  expand  them  equally,  and  for 
every  degree  of  Fahrenheit's  thermometer  they  increase  about 

*  For  a  more  extended  view  of  conduction  and  radiation  of  caloric,  see 
Gray's  Chemistry,  Caloric,  p.  26. 

What  is  the  fundamental  property  of  sensible  caloric  ?  How  are  solids 
heated?  How  liquids  and  gases  ?  Define  conduction  and  radiation.  What 
generic  effect  produced  by  caloric  ? 


SENSIBLE   AND    INSENSIBLE    CALORIC.  249 

of  what  their  volume  would  be  at  32°,  on  the  supposition 
that  they  do  not  condense  at  that  temperature. 

III.  Insensible  Caloric  exists  in  different  quantities  in  differ- 
ent substances,  while  their  temperature  is  exactly  the  same  ;  and 
as  any  body  changes  its  form,  its  power  of  retaining  insensible 
caloric  is  increased  or  diminished,  so  that  caloric  will  pass  from 
its  sensible  to  its  insensible  state,  and  the  reverse,  as  the  forms 
of  matter  change. 

The  principal  effects  of  insensible  caloric  are  to  produce  lique- 
faction and  vaporization. 

1 .  When  sensible  caloric  is  applied  to  a  solid,  as  lead,  at  a  cer- 
tain temperature,  the  solid  melts,  but  after  it  has  arrived  at  the 
melting  point,  which  is  always  the  same  in  the  same  substance, 
an  additional  quantity  of  caloric  must  be  passed  into  an  insensible 
state  before  liquefaction  can  be  effected.    Thus  ice,  when  brought 
to  the  temperature  of  32°  F.,  its  melting  point,  will  still  retain 
the  solid  state  until  sufficient  caloric  is  added  to  raise  it,  if  it 
continued  ice,  to  172°  F.,  or  140  degrees  of  sensible  caloric  must 
pass  into  the  insensible  state  before  the  ice  will  become  water. 

2.  The  same  also  takes  place  when  liquids  are  heated  to  the 
point  of  vaporization.     Before  they  assume  the  state  of  vapor, 
there  must  be  added  a  large  quantity  of  free  caloric  to  pass  into 
an  insensible  state.     Thus  water,  if  heated  to  212°,  its  boiling 
point,  will  not  assume  the  state  of  vapor  or  steam  until  nearly 
1000°  of  free  caloric  are  supplied  to  pass  into  an  insensible  state. 

When  vapors  are  condensed  into  liquids,  and  liquids  are  con- 
gealed to  solids,  this  insensible  caloric  becomes  free,  or  is  driven 
out  of  the  body,  and  appears  again  in  the  sensible  state. 

IV.  Steam. — The  formation  of  steam  by  the  agency  of  caloric, 
and  its  employment  as  a  mechanical  power  in  connection  with 
the  steam-engine,  render  a  knowledge  of  its  properties  essential  to 
a  clear  understanding  of  the  manner  by  which  its  useful  effects 
are  produced. 

1 .  Steam  is  formed  at  all  temperatures,  but  it  is  only  when  it  is 
formed  at  the  temperature  of  the  ebullition  of  water,  and  confined 

What  is  insensible  caloric,  and  what  are  its  effects?  Illustrate  these 
effects.  What  is  steam,  and  how  formed  ? 

L  2 


250  NATURAL    PHILOSOPHY. 

in  some  appropriate  vessel,  that  its  force  can  be  employed  for 
any  valuable  mechanical  purpose.  When  water  is  heated  to 
212°  F.  in  an  open  vessel,  it  assumes  the  state  of  steam,  in  doing 
which  it  must  exert  a  pressure  equal  to  that  of  the  atmosphere, 
or  15  Ibs.  to  every  square  inch.  If  a  quantity  of  steam  thus 
formed  is  conducted  into  a  close  vessel  of  the  same  temperature, 
212°,  and  heat  applied  to  it,  it  will  expand,  or  tend  to  expand, 
in  precisely  the  same  manner  as  atmospheric  air ;  for  if  it  were 
placed  in  a  bag,  and  the  pressure  of  the  atmosphere  entirely  re- 
moved, it  would  tend  to  expand  indefinitely.  If,  however,  we 
attempt  to  apply  pressure  to1  steam  at  212°  F.,  or  to  remove 
pressure  from  it,  it  will  be  condensed,  and  return  to  the  fluid 
state.  At  this  point  of  condensation  the  steam  is  said  to  have 
its  maximum  of  tension,  and  if  it  is  formed  at  higher  tempera- 
tures under  the  influence  of  pressure,  at  the  point  it  would  con- 
dense it  has  its  maximum  of  tension  ;  hence 

The  tension  of  steam  will  depend  upon  the  temperature  at 
^vhich  it  informed. 

2.  But  we  can  not  determine  the  tension  of  steam,  or  its  elastic 
force  at  different  temperatures,  without  attending  to  the  condi- 
tions under  which  it  is  formed  in  the  boiler  ;  for,  as  the  tempera- 
ture is  increased,  portions  of  steam  are  constantly  added  by  the 
vaporization  of  the  water,  which  renders  it  necessary  to  resort  to 
experiment  in  order  to  ascertain  its  increase  of  tension  with  the 
increase  of  temperature. 

This  may  be  effected  by  employing  a  strong 
boiler  called  a  Digester,  a,  Fig.  206,  partly  filled 
with  water.  A  thermometer,  d,  passes  into  the 
water  to  ascertain  the  temperature,  and  a  glass 
tube,  c,  extends  to  the  bottom,  and  dips  into  a 
quantity  of  mercury  under  the  water.  If  now 
this  bulb  be  heated  by  a  spirit  lamp,  and  the  wa- 
ter be  made  to  boil,  the  air  being  all  let  out  by 
the  stop-cock  b,  at  the  moment  the  water  reaches 
its  point  of  ebullition,  212°  F.,  the  tensioii  of  its 
steam  will  be  just  equal  to  that  of  the  atmos- 

What  law  of  expansion  does  stefcm  observe  on  increase  of  temperature  ? 
Upon  what  does  the  tension  of  steam  depend  ?  How  is  the  pressure  of 
steam  as  the  temperature  rises  ascertained  ?  Describe  the  digester 


TENSION    OF    STEAM. 


251 


phere ;  and  as  that  pressure  is  exerted  by  the  air  in  the  tube  c, 
the  mercury  will  remain  at  the  same  point  as  when  the  air  was 
in  the  upper  part  of  the  globe  instead  of  the  steam. 

If  now  we  raise  the  tempera  ure  to  about  249°  F.,  the  mer- 
cury in  the  tube  will  be  raised  1 1  the  height  of  30  inches,  the 
pressure  on  the  surface  of  the  watei  is  doubled,  and,  of  course,  the 
elastic  force  of  the  steam,  its  tension,  will  be  equal  to  two  atmos- 
pheres of  pressure,  or  30  Ibs.  to  the  square  inch.  By  increasing 
the  temperature,  we  shall  find  that  the  tension  increases  with 
increase  of  temperature,  as  in  the  following  table  : 

At  the  temperature  of  212°  F.,  the  tension  is  equal  to    1  atmosphere. 


249° 
293° 
320° 
.341° 
359° 
392° 
438° 
456° 


2 
4 
6 
8 
10 
15 
25 
30 


(Mutter,} 

If  water  is  confined  under  the  pressures  indicated  in  the  above 
table,  its  boiling  temperature  will  vary  according  to  the  same 
law  of  temperature  as  the  tension  of  its  vapor,  so  that  its  boiling 
point  under  a  pressure  of  30  atmospheres  would  be  456°  F. 

It  will  be  seen  by  inspecting  the  above  table  that  the  tension 
of  steam  increases  much  more  rapidly  in  the  higher  than  in  the 
lower  temperatures.  Thus,  between  212°  and  249°  F.,  a  rise  of 
37°  only  doubles  the  tension,  or  renders  it  equal  to  2  atmospheres ; 
but  from  438°  to  456°  F.,  a  jise  of  18°,  the  increase  of  tension  is 
equal  to  5  atmospheres.  This  rapid  increase  of  tension  is  due  to 
the  greater  density  of  the  steam,  which  gives  it  a  greater  elastic 
force.  This  is  shown  by  the  fact  that  a  cubic  inch  of  water,  when 
converted  into  steam  at  212°,  will  occupy  a  space  equal  to  1700 
cubic  inches  ;  but  if  it  is  converted  into  steam  at  a  temperature 
of  249°  F.,  it  will  only  yield  897  cubic  inches  ;  and  if  the  tem- 
perature be  359°  when  it  is  converted  into  steam,  it  will  then  oc- 
cupy only  207  cubic  inches.  Hence,  as  it  occupies  much  less 
space,  its  density  must  be  much  greater  when  formed  at  high  than 
at  low  temperatures ;  and  if  there  were  no  additional  steam  added, 

What  effect  has  pressure  upon  the  boiling  point  of  water? 


252 


NATURAL    PHILOSOPHY. 


there  would  be  an  increase  of  tension  from  an  increase  of  tem- 
perature. For  these  two  reasons,  therefore,  the  tension  increases 
more  rapidly  as  the  temperature  is  higher. 

3.  When  steam  is  formed  at  any  temperature,  at  its  maximum 
of  tension  a  sudden  and  slight  reduction  of  temperature  will  con- 
dense it.  By  means  of  a  jet  of  cold  water,  the  steam  in  the  cyl- 
inder of  the  low  pressure  steam-engine  is  condensed,  and  it  is 
due  to  this  property  of  steam  that  low  pressure  engines  are  capa- 
ble of  being  worked. 

From  this  rapid  increase  of  tension  or  pressure  as  the  temper- 
ature is  higher,  there  would  seem  to  be  a  practical  advantage  in 
using  steam  under  high  pressure  ;  that  is,  if  we  wish  to  pro- 
duce a  given  constant  force,  it  can  be  done  with  much  less  fuel 
under  a  high  than  under  a  low  temperature ;  for  the  insensible 
caloric  diminishes  as  the  temperature  increases,  so  that  in  the 
same  weight  of  steam  the  sum  of  sensible  and  insensible  caloric 
is  constant,  and  yet  there  is  so  much  danger  at  such  high  tem- 
peratures of  bursting  the  boiler  as  to  render  it  impracticable  to 
secure  the  advantage.  A  pressure  of  two  or  three  atmospheres 
is  sufficient  for  the  ordinary  purposes  to  which  steam  power  is 
applied. 

V.  Steam- Engine.  —  The  steam-engine  owes 
its  present  perfection  to  Mr.  James  Watt.  In  or- 
der to  understand  the  principle  by  which  steam  is 
applied  in  the  engine,  it  is  only  necessary  to  take  a 
glass  tube,  with  a  bulb  and  solid  piston  capable  of 
working  up  and  down  in  the  tube,  A^B,  Fig.  207. 
By  heating  the  water  in  A  with  a  spirit  lamp, 
the  steam  formed  will  raise  the  piston  to  the  top ; 
then,  by  immersing  the  bulb,  A,  in  cold  water,  it 
will  condense  the  steam,  and  the  force  of  the  at- 
mosphere will  drive  the  piston  to  the  bottom. 
Now  if,  by  means  of  a  tube  connected  with  a  steam 
boiler,  the  steam  be  admitted  at  the  bottom  below 
the  piston,  it  will  raise  it  up  as  before ;  but,  in  order 
to  condense  it,  its  temperature  must  be  reduced. 
This  may  be  effected  by  stopping  the  supply  of  steam ;  and,  by 

How  may  steam  be  condensed  ?  By  what  experiment  may  the  princi- 
ple of  the  steam-engine  be  illustrated  7 


LOW    AND    HIGH    PRESSURE    ENGINES.  253 

means  of  a  tube  in  the  side,  introducing  a  small  jet  of  cold  wa- 
ter, the  pressure  of  the  atmosphere  will  again  force  the  piston 
to  the  bottom  ;  on  readmitting  the  steam,  it  will  be  forced  up. 
This  may  illustrate  one  form  of  the  Zo^-pressure  engine.  It  will 
be  seen  that  the  piston  must  be  forced  up  against  the  pressure  of 
the  atmosphere,  and  hence  the  steam  must  have  considerable 
tension ;  but  if  the  piston  rod  is  made  to  move  through  a  steam- 
tight  collar,  and  the  steam  introduced  and  condensed  at  the  top 
of  the  cylinder  as  well  as  at  the  bottom,  the  same  motion  may 
be  produced  with  much  less  power  ;  as  the  whole  pressure  of  the 
atmosphere  is  removed,  the  piston  will  be  forced  up  by  a  force 
less  by  15  Ibs.  to  the  square  inch,  but  when  it  is  at  the  top  we 
must  apply  the  same  force  to  press  it  to  the  bottom.  Hence,  as 
the  engine  is  worked  with  a  lower  power  of  steam,  it  is  called  a 
low-pressure  engine,  and  the  improvement  of  Watt  consisted 
chiefly  in  condensing  the  steam  in  a  separate  vessel  called  a  con- 
denser, so  that  the  temperature  of  the  cylinder  was  kept  uniform. 

The  high-pressure  engine  is  the  same  in  all  respects,  except- 
ing that  the  steam  is  not  condensed,  but  is  passed  out  at  the  bot- 
tom and  top  of  the  cylinder,  through  appropriate  valves,  which 
are  opened  and  closed  by  the  motion  of  the  piston.  The  same 
motion  also  admits  and  shuts  off  the  steam  at  the  bottom  and  top 
of  the  cylinder.  As  these  engines  work  against  the  pressure  of 
the  atmosphere,  they  require  a  high  tension  of  steam,  and  hence 
are  called  high-pressure  engines. 

High-pressure  engines  are  used  in  the  steam -boats  on  our  West- 
ern rivers  and  lakes,  whether  this  is  due  to  the  opinion  that  the 
mud  which  collects  in  the  boiler  and  other  parts  of  the  machinery 
is  more  inconvenient  in  low  than  in  high-pressure  engines,  or 
whether  it  arises  from  some  other  cause.  We  have  lately  seen 
an  invention  which  will  remedy  the  inconvenience,  by  filtering  the 
water  as  it  enters  the  boiler.  When  the  steam  escapes  it  gives 
rise  to  successive  puffs,  which  may  be  heard  at  a  great  distance. 
Locomotives  have  also  high-pressure  engines.  One  reason  for 
this  is,  they  may  be  made  to  occupy  less  space.  Low-pressure 

Describe  the  low-pressure  engine  ;  the  high-pressure.  What  engines  are 
used  on  our  Western  waters  ?  What  kind  of  engines  are  used  in  locomotives  ? 


NATURAL    PHILOSOPHY. 

engines  have  a  more  complicated  apparatus  attached  to  them  for 
condensing  the  steam,  and  are  generally  used  in  all  large  stearu 
vessels. 

Connected  with  the  cylinder  and  piston  there  is  a  very  compli- 
cated apparatus,  as  a  boiler,  pumps,  wheels,  &c.,  "which  consti- 
tute what  is  called  the  Steam-Engine. 

1.  The  Boiler. — The  steam  boiler  is  made  in  the  form  of  a 
cylinder,  out  of  plates  of  sheet  iron  strongly  riveted  together. 
Sometimes  tubes  extend  through  the  boiler,  to  allow  the  heat  to 
be  more  readily  and  equally  diffused.  The  following  cut,  Fig. 
208,  will  give  a  very  good  idea  of  the  boiler  and  its  fixtures. 
Thus,  B  B  is  the  boiler,  the  lower  part  containing  water,  and  the 
upper  portion,  S  S,  steam  ;  F  B  is  the  fire.  When  coal  is  used, 
the  fire  is  kept  up  by  means  of  a  blower,  consisting  of  a  fan- 
wheel,  which,  being  rapidly  turned  by  the  machinery,  forces  the 
air  through  a  tube  constructed  for  the  purpose. 


(1.)  To  determine  the  elastic  force  of  the  steam,  or  pressure,  as 
it  is  called,  there  is  both  a  barometer  gauge  at  M,  and  a  safe- 
ty valve  in  the  center,  e  a  b.  This  valve,  which  is  of  a  conical 

Describe  the  boiler.     How  is  the  pressure  determined  1 


THE    STEAM    BOILER.  255 

shape,  is  attached  to  a  rod,  connected  with  a  lever  of  the  third 
kind,  e  being  the  fulcrum,  a  the  point  where  the  force  of  the  steam 
is  applied,  and  w  the  weight  capable  of  sliding  on  a  b.  As  this 
lever  is  graduated  like  a  steelyard,  the  force  of  the  steam  may  be 
accurately  weighed.  It  also  serves  another,  which  is  its  princi- 
pal purpose,  that  of  a  safety  valve;  for  when  the  pressure  arrives 
at  a  certain  degree  of  intensity,  the  valve  is  forced  up  and  the 
steam  rushes  out,  and  thus  the  boiler  is  protected  from  being 
burst  by  the  elastic  force  of  the  steam. 

(2.)  But  it  sometimes  liappens  that  the  steam  loses  its  tension, 
or  becomes  condensed  by  the  addition  of  too  much  cold  water, 
and  the  boiler  then  is  liable  to  be  forced  in  by  the  pressure  of  the 
atmosphere.  To  guard  against  this,  there  is  another  valve  at  U, 
which  opens  downward,  and  allows  the  air  to  rush  in  whenever 
the  boiler  is  exposed  to  a  collapse.  L  is  a  large  opening,  firmly 
closed  excepting  when  it  is  desirable  to  clean  the  boiler,  as  it  be- 
comes incrusted  with  salt  or  mud. 

(3.)  To  determine  the  height  of  ivater  in  the  boiler,  two  tubes, 
with  stop-cocks,  c  d,  are  inserted;  one  of  them  dips  just  below  the 
water  level,  and  the  other  passes  into  the  steam  just  above  the 
water  level ;  if  the  water  sinks  too  low,  steam  will  issue  from 
each  pipe ;  if  too  high,  water  will  be  forced  through  both  of  them. 

(4.)  To  regulate  the  supply  of  ivater  as  it  is  constantly  passed 
off  in  steam,  there  is  a  feed-pipe.  This  consists  of  a  pipe,  v  o, 
which  extends  nearly  to  the  bottom  of  the  boiler,  having  a  valve, 
v,  which  is  opened  and  closed  by  the  lever  b  c  a.  The  lever 
has  attached  to  it  a  rod,  which  passes  into  the  boiler,  and  is  ter- 
minated by  a  square  block  or  stone,  B,  resting  on  the  surface  of 
the  water  in  the  boiler,  and  counterpoised  by  a  weight,  p.  This 
lever  turns  upon  the  fulcrum  c.  If  the  water  rises  in  the  boiler, 
it  lifts  the  end  of  the  lever  «,  and  closes  the  valve  v,  which  pre- 
vents the  water  from  flowing  in  through  the  pipe ;  but  if  the  wa- 
ter sinks,  it  depresses  a,  which  lifts  the  valve,  and  allows  a  sup- 
ply to  flow  into  the  boiler.  By  this  means  the  water  in  the  boil- 
er is  kept  at  the  same  height. 

How  may  a  collapse  be  prevented  ?  By  what  arrangement  can  the 
height  of  the  water  in  the  boiler  be  ascertained  ?  How  is  the  supply  of 
water  regulated  ? 


NATURAL    PHILOSOPHY. 


(5.)  To  convey  the  steam  to  the  engine  there  is  a  steam-pipe,  s, 
with  a  valve,  v,  which  may  be  used  to  regulate  the  supply  of 
steam  by  opening  and  closing  it  with  the  hand,  or  by  means  of 
the  governor,  which  is  attached  to  the  revolving  parts  of  the  ma- 
chinery (see  page  255). 

2.    The  Steam-Engine,  Fig.  209. 


Fig.  209. 


(1.)  The  steam  is 
conducted  through 
the  steam -pipe,  s, 
which  comes  from 
the  boiler  through 
the  four-way  cock, 
a,  where  the  tube 
branches,  one  pass- 
ing into  the  cylin- 
der, c,  near  the  bot- 
tom, and  the  other 
near  the  top,  so  that 
by  means  of  a  valve 
connected  with  the 
levers  yy,  the  steam 
may  be  sent  altern- 
ately above  and  be- 
low the  piston  as 
the  machinery  is  put 
in  motion.  The  pis- 
ton-rod is  attached  to  the  end  of  the  working-beam,  B  F,  which 
moves  upon  the  fulcrum  or  pivot,  A.  A  rod,  F  R,  is  also  attach- 
ed, either  to  the  crank  of  the  fly-wheel,  H  H,  with  which  the 
other  revolving  parts  communicate,  or  directly  to  the  crank  of  the 
wheel,  which,  as  in  the  steam-boat,  bears  the  floats  upon  the  ex- 
tremities of  its  axle. 

(2.)  Escape  of  Steam. — In  the  high-pressure  engine,  after  the 
steam  admitted  into  the  lower  part  of  the  cylinder  has  raised  the 
piston,  it  passes  out  through  a  valve  in  the  bottom,  which  opens 
at  the  moment  the  steam  is  let  in  at  the  top  to  force  the  piston 
down  ;  a  similar  valve  discharges  the  steam  which  is  above  the 
piston  as  it  rises.  In  the  low-pressure  engine,  the  steam  above 
and  below  the  piston  is  condensed  at  each  stroke. 

(3.)  Condenser. — For  this  purpose  there  is  a  condenser,  J,  im- 

How  i3  the  supply  of  steaai  regulated  ?  How  is  the  steam  introduced 
into  the  cylinder  ?  What  becomes  of  the  steam  in  high-pressure  engines  ? 
How  is  it  disposed  of  in  low-pressure  engines  ? 


THE    STEAM-ENGINE.  257 

mersed  in  a  cistern  of  cold  water,  and  with  pipes,  ff,  which  are 
connected  with  the  bottom  and  top  of  the  cylinder,  to  allow  the 
steam  to  flow  into  it  as  the  piston  works  up  and  down  in  the 
cylinder. 

In  this  vessel  the  steam  is  condensed  by  a  jet  of  cold  water, 
which  is  thrown  from  the  injection  cock.  The  water  thus  con- 
densed is  pumped  by  the  air  pump,  O,  into  the  well,  W,  from 
whence  it  is  again  pumped  into  the  pipe  i  i,  which  leads  to  the 
feed-pipe.  By  this  means  warm  water  is  constantly  supplied 
to  the  boiler,  and  this  occasions  a  great  saving  of  fuel  in  work- 
ing the  engine. 

(4.)  Regulation  of  the  Steam. — The  supply  of  steam  is  regu- 
lated by  the  governor,  G  (p.  111).  The  valves  which  admit  the 
steam  above  or  below  the  piston  in  the  cylinder  are  closed,  and 
the  steam  shut  off  when  the  piston  has  traversed  half  or  three 
quarters  of  the  distance  from  the  top  to  the  bottom  or  the  bottom 
to  the  top.  If  the  steam  were  to  flow  till  the  piston  had  reach- 
ed its  highest  or  lowest  point,  there  would  be  an  irregularity  in 
its  motion,  and  a  sudden  jar  at  each  stroke  ;  but  by  shutting  off 
the  steam  at  a  certain  point,  the  motion  is  quite  uniform.  There 
is  also  a  great  saving  of  power,  as  it  requires  much  less  steam  to 
work  the  piston. 

(5.)  The  power  of  the  engine  depends  very  much  upon  the  size 
of  its  cylinder  and  the  length  of  the  stroke.  If  we  know  the 
tension  or  pressure  of  the  steam  and  the  area  of  a  section  of  the 
cylinder,  we  may  determine  the  force  of  its  stroke,  or  the  force 
which  is  exerted  upon  it  by  the  steam.  It  is  found,  however, 
that  much  of  this  force  is  lost  before  it  is  transmitted  to  the  re- 
volving parts  of  the  machinery.  The  power  is  estimated  by  com- 
paring it  with  horse  power,  on  the  supposition  that  a  horse  will 
exert  a  force  in  the  space  of  one  minute  which  will  raise  33,000 
Ibs.  one  foot  in  height.  Thus  we  have  engines  of  2,  5,  and  20 
horse  power. 

"  The  steam-engine  appears  to  be  a  thing  almost  endowed  with 
intelligence.  It  regulates  with  perfect  accuracy  and  uniformity 
the  number  of  its  strokes  in  a  given  time,  counting  and  record- 
ing them,  moreover,  to  tell  how  much  work  it  has  done,  as  a 
clock  records  the  beats  of  its  pendulum.  It  regulates  the  quan- 

How  is  the  steam  condensed  in  the  low-pressure  engine  ?  How  is  the 
power  of  the  engine  estimated  t 


258  NATURAL    PHILOSOPHY. 

tity  of  steam  admitted  to  work  ;  the  briskness  of  the  fire ;  the 
supply  of  water  to  the  boiler ;  the  supply  of  coals  to  the  fire. 
It  opens  and  shuts  its  valves  with  absolute  precision  as  to  time 
and  manner ;  it  oils  its  joints  ;  it  takes  out  any  air  which  may 
accidentally  enter  into  parts  which  should  be  vacuous  ;  and 
when  any  thing  goes  wrong  which  it  can  not  of  itself  rectify,  it 
warns  its  attendants  by  ringing  a  bell.  Yet  with  all  these  tal- 
ents and  qualities,  and  even  when  exerting  the  force  of  hundreds 
of  horses,  it  is  obedient  to  the  hand  of  a  child.  Its  aliment  is 
coal,  wood,  charcoal,  or  other  combustibles.  It  consumes  none 
while  idle.  It  never  tires,  and  wants  no  sleep.  It  is  not  sub- 
ject to  malady  when  originally  well  made,  and  only  refuses  to 
work  when  worn  out  with  age.  It  is  equally  active  in  all  climes, 
and  will  do  work  of  any  kind.  It  is  a  water  pumper,  a  miner, 
a  sailor,  a  cotton-spinner,  a  weaver,  a  blacksmith,  a  miller,  &c. ; 
and  a  small  engine,  in  the  character  of  a  steam  pony,  may  be 
seen  dragging  after  it  on  a  rail-road  a  hundred  tons  of  merchan- 
dise, or  a  regiment  of  soldiers,  with  thrice  the  speed  of  our  fleet- 
est horse  coaches.  It  is  a  king  of  machines,  and  a  permanent 
realization  of  the  genii  of  Eastern  fable,  submitting  supernatural 
powers  to  the  command  of  man," — Arnott. 


CHAPTER  VIII. 

ELECTRICITY. 

THE  term  electricity  is  derived  from  the  Greek-  name*  of  am- 
ber, a  substance  which,  on  being  rubbed  with  a  woolen  or  silk 
cloth,  has  the  property  of  attracting  light  bodies. 

History.-  —  The  first  recorded  discovery  of  this  property  was 
made  by  Thales  of  Miletus,  who  lived  about  six  hundred  years 
before  the  Christian  era  ;  but  nothing  important  was  known  of 
the  subject  until  the  commencement  of  the  seventeenth  century. 

Dr.  Gilbert,  in  1600,  made  some  few  observations.     Boyle,  a 


Meaning  of  electricity.     History  of  electricity. 


ELECTRICITY.  259 

half  century  later,  made  a  few  additional  discoveries ;  but  the 
science  was  not  systematized  until  the  time  of  Franklin,  Gray, 
and  Du  Fay,  between  the  years  1730  and  1760.  Since  this 
time  electricity  has  attracted  much  of  the  attention  of  philoso- 
phers, and  is  now  one  of  the  most  beautiful  and  interesting 
branches  of  physical  science. 

Amber  is  not  the  only  substance  capable  of  exhibiting  the 
phenomena  of  attraction  when  friction  is  employed,  but  a  great 
many  other  substances  have  this  same  property.  Glass  and  res- 
inous substances,  as  a  glass  rod  or  a  piece  of  sealing-wax,  when 
rubbed,  furnish,  perhaps,  the  readiest  means  for  exhibiting  the 
presence  of  the  electric  fluid,  as  the  unknown  cause  of  this  pecu- 
liar attraction  is  called. 

When  any  body  is  rubbed  and  electricity  is  produced,  it  is  said 
to  be  excited,  or  electrically  excited ;  and  if  any  other  body  re- 
ceive the  fluid  from  it,  that  body  is  said  to  be  electrified. 

Electricity  is  excited,  however,  in  a  variety  of  ways,  and  there 
are  found  to  be  certain  modifications  of  its  properties,  dependent 
upon  the  mode  of  generating  it.  The  two  methods  which  pro- 
duce the  greatest  difference  are  friction  arid  chemical  action. 
The  former  gives  rise  to  Statical  or  Common  Electricity,  and  the 
latter  to  Voltaic  Electricity,  or  Galvanism. 

SECTION  I.— STATICAL  OR  COMMON  ELECTRICITY. 

I.  Electricity  is  excited  by  friction,  by  change  of  form  and 
temperature,  by  pressure,  and  by  chemical  and  vital  action. 

II.  Electricity  is  detected  by  electroscopes,  and  its  force  meas- 
ured by  electrometers. 

III.  It  consists  oftivo  kinds,  called  positive  and  negative,  also 
vitreous  and  resinous.      The  positive  is  produced  by  rubbing 
glass  and  other  vitreous  bodies,  and  the  negative  by  friction  upon 
amber  and  other  resinous  matter.      These  substances  are  called 
non-conductors,  while  the  metals,  water,  and  some  other  bodies 
are  termed  conductors. 

IV.  The  generic  property  of  the  electric  fluids  is,  that  each 

What  other  substances  yield  it  ?  Meaning  of  electrically  excited  and 
electrified. 


260  NATURAL    PHILOSOPHY. 

repels  itself  and  attracts  the  other,  so  that  the  presence  of  the  one 
induces  that  of  the  other,  a  process  called  induction. 

V.  Free  electricity  resides  on  the  surface  of  conductors,  and 
does  not  penetrate  their  substance  ;  hence  the  quantity  will  de- 
pend upon  the  extent  of  surface.     In  a  sphere  it  is  equally  dis- 
tributed, but  in  a  spheroid  it  accumulates  near  the  extremities, 
and  floivs  into  the  air  from  points,  so  as  to  prevent  a  pointed 
conductor  from  retaining  it. 

VI.  In  the  Ley  den  jar,  the  two  electricities  are  held  on  opposite 
sides  of  glass  by  the  force  of  their  mutual  attraction,  by  which 
arrangement  electricity  may  be  accumulated  in  much  greater 
quantities,  and  made  to  exhibit  its  effects  with  greater  power. 

VII.  Electricity  is  capable  of  producing  powerful  effects,  me- 
chanical, chemical,  and  vital.. 

VIII.  The  atmosphere  is  ahuays  electrified  in  various  degrees. 
In  it  the  most  sublime  displays  of  electricity  are  witnessed  in 
the  phenomena  of  thunder  storms  ;  and  as  electricity  often  pass- 
es from  the  clouds  to  the  earth,  its  injurious  effects  may  be  avoid- 
ed by  means  of  lightning  rods,  which  will  convey  it  silently  to 
the  earth,  and  thus  prevent  buildings  from  being  rent  by  the 
"  lightning  stroke." 

I.  Modes  of  producing  Electricity . — 1.  By  fric-       fig- mo- 
tion of  one  body  upon  another  electricity  is  always 
generated. 

Thus  the  friction  of  two  solids,  as  woolen  cloth 
on  a  rod  of  glass  or  resin,  a,  Fig.  210,  causes  both 
bodies  to  be  excited,  and  they  will  attract  light  bod- 
ies, as  b,  if  brought  near  to  them. 

The  effect  of  friction  on  different  bodies  is  very  dissimilar. 
Some  retain  the  fluid  on  their  surfaces,  and  do  not  permit  it  to 
pass  from  one  point  to  another.  Hence  they  are  called  non-con- 
ductors and  insulators.  All  vitreous  and  resinous  bodies,  such 
as  sulphur,  silk,  wool,  feathers,  and  dry  wood,  arc  non-conduct- 
ors. Others  permit  it  to  pass  with  greater  or  less  facility  over 
their  surfaces,  take  it  readily  from  non-conducting  substances, 

How  is  electricity  produced  ?  What  are  conductors  and  non-conductors 
of  electricity  ? 


MODES    OF    PRODUCING    ELECTRICITY.  261 

and  impart  it  to  other  conductors  with  little  or  no  obstruction. 
Bodies  of  this  class  are  called  conductor?,  of  electricity.  Met- 
als are  the  best  conductors ;  and,  though  the  effect  of  friction  upon 
them  is  to  excite  electricity,  yet  it  passes  off  readily  unless  they 
are  surrounded  by  insulators.  Resinous  and  vitreous  bodies  are 
those  generally  employed  for  exciting  electricity,  and  hence  are 
called  electrics* 

2.  The  friction  of  tivo  liquids,  or  a  liquid  with  a  solid,  also 
excites  electricity  ;  but,  as  most  liquids  are  good  conductors,  it  is 
conveyed  away  as  fast  as  it  is-  produced. 

Gases,  also,  by  friction  upon  each  other,  or  upon  solid  or  liq- 
uid bodies,  develop  this  fluid ;  thus,  when  the  air  blows  over  the 
frozen  ground,  or  when  steam  of  high  tension  issues  from  a  steam 
boiler,  great  quantities  are  produced.  But  friction,  though  the  best 
and  most  common  mode  of  exciting  electricity,  is  not  the  only  mode. 

3.  Electricity  is  excited  by  change  of  form  in  bodies.     Thus, 
when  water  congeals  or  ice  melts,  or  when  water  evaporates  or 
is  condensed  in  the  atmosphere,  large  quantities  of  electricity  are 
excited.     The  same  is  true  of  all  other  bodies  which  undergo  a 
change  of  state. 

4.  Electricity  is  excited  by  the  pressure  of  one  body  upon  an- 
other, or  by  mere  contact,  so  that  we  can  not  place  our  hand  upon 
any  substance  without  exciting  the  electric  fluid,  though  in  a 
degree  requiring  a  special  apparatus  in  order  to  detect  it. 

5.  Electricity  is  also  excited  by  chemical  action,  or 
by  the  decomposition  of  bodies.  Thus,  if  a  copper  and 
zinc  plate  be  immersed  in  acidulated  water,  Fig.  211, 
and  their  edges  be  brought  together  by  means  of  a  wire, 
d,  electricity  will  be  excited  in  currents  flowing  from  one 
plate  to  the  other.  This  kind  of  electricity  is  called 
Galvanic  or  Voltaic  Electricity,  and  possesses  many 
peculiar  properties  which  distinguish  it  from  the  preceding  kinds. 

6.  Heat  is  another  means  of  producing  electric  currents. 

7.  Some  animals  also  have  the  power  of  generating  electricity 
by  means  of  organs  which  resemble  the  galvanic  battery. 

Why  are  not  liquids  used  to  generate  electricity  ?     How  is  electricity 
excited  by  gases?     Mention  the  other  modes  of  exciting  electricity. 


262 


NATURAL    PHILOSOPHY. 


The  three  latter 'modes  will  be  considered  under  Galvanism. 

From  the  above  statements,  it  is  evident  that  electricity  per- 
vades all  matter,  liquids,  solids,  and  gases,  though  it  sustains  very 
different  relations  to  two  great  classes  of  bodies,  which  are  distin- 
guished by  the  terms  conductors  and  non-conductors,  or  insulators. 

No  substance,  however,  is  a  perfect  non-conductor.  The  pow- 
er of  insulating  and  of  conducting  electricity  is^possessed  by  the 
two  classes  of  substances  in  very  different  degrees.  The  follow- 
ing table  exhibits  the  most  important  substances  in  the  two  classes  : 


Conductors. 

The  Metals  are  the  best. 

Charcoal, 

Plumbago, 

Pure  Water, 

Moist  Snow, 

Steam  and  Smoke, 

Vegetables, 

Animals. 


Non-Condnctors. 

Resins,  Shell-lac  are  the  best. 

Amber,  Sulphur, 

Wax,  Fat, 

Glass  and  precious  Stones, 

Silk,  Wool,  Hair,  Feathers. 

Cotton,  Paper, 

Diy  Air,  Baked  Wood, 

Indii 


Fig.  214. 


Lia  Rubber. 

II.  Modes  of  detecting  Electricity. — The  instruments  by  which 
the  presence  of  electricity  is  detected  are  called  electro-  Fig.  213. 
scopes.  Those  by  which  its  force  is  measured  are  term- 
ed electrometers.  But  the  term  electrometer  is  generally 
used  for  both  kinds. 

An  electrometer  may  be  a  pith  ball  suspended  to  a 
rod  by  a  thread,  called  the  Pendulum  Electrometer,  or  a 
pith  ball  on  the  end  of  a  pointer,  attached  to  an  index, 
called  the  Quadrant  Electrometer,  Fig.  213,  or  two  strips 
of  metal,  as  gold  leaf,  called  the 

Gold  Leaf  Electroscope. — This  instrument  consists 
of  a  glass  jar,  d,  Fig.  214,  in  which  two  strips  of  gold 
leaf  are  hung  side  by  side,  attached  to  a  metallic  rod, 
b,  which  is  terminated  by  a  disc,  a,  or  a  knob ;  a  cup 
and  point,  c,  may  also  be  applied  to  the  disc.  Two 
pieces  of  tin  foil  are  placed  on  the  inside  of  the  jar,  as 
d,  to  discharge  the  electricity,  if  the  leaves  diverge 
sufficiently  to  touch  them. 

The  most  delicate  instrument  for  detecting  small 
quantities  of  electricity  is 

'Bohnenberger  's  Electroscope,  Fig.  215,  which  con- 

What  are  electroscopes  1  electrometers  ?     Describe  the  gold  leaf  elec- 
troscope— Bohnenberger's. 


ELECTROSCOPES. 


263 


Fig.  215. 


sists  of  one  strip  of  gold  leaf,  arranged  as  above, 
and  suspended  between  two  metallic  plates,  p  m. 
These  plates  are  connected  by  wires  to  a  dry  pile, 
a  b,  which  is  formed  by  a  series  of  small  circu- 
lar plates,  each  consisting  of  gold  leaf  and  zinc, 
with  a  piece  of  paper  between  them.  They  are 
packed  closely  in  a  glass  tube,  so  that  the  metals 
shall  alternate  with  each  other.  By  this  means 
electricity  will  be  excited,  so  that  the  plates  p  and 
m  will  be  constantly  in  opposite  states,  and  the 
leaf,  being  equally  attracted,  remains  suspended  between  them  ; 
but  by  communicating  the  slightest  trace  of  electricity  to  o  n,  the 
leaf  will  move  to  p  or  m,  according  to  the  kind  of  electricity 
which  is  applied. 

III.  Electrical  States  produced  by  Friction  of  different  Sub- 
stances. —  By  means  of  the  gold  leaf  electroscopes  above  describ- 
ed, or  simply  by  pith  balls  suspended  by  silk  threads,  we  may  ex- 
hibit, experimentally,  the  first  fundamental  facts  which  were 
noticed  in  reference  to  the  electric  fluid. 

Fig.  216.  Exp.  —  If  a  glass  rod  is  rubbed  with  silk  or  with  a  wool- 

x  —  x  en  cloth,  and  brought  near  the  pith  ball  electroscope,  Fig. 

\  __      216,  the  ball  will  be  attracted  toward  it,  remain  in  contact 
0  ~^)    a  moment,  and  then  recede  or  be  repelled.     If  a  second  ball 

C\  <BP"  he  electrified  by  the  rod  in  the  same  manner,  the  two  elec- 
trified balls  will  mutually  repel  each  other. 

Exp.  —  If  a  piece  of  sealing-wax  be  used  instead  of  the 
glass  rod,  the  same  effects  will  be  produced.     Each  ball  will 
at  first  be  attracted  and  then  recede,  and  when  the  two  balls 
are  brought  near  each  other,  a  mutual  repulsion  will  take 
place. 

Exp.  —  If  one  of  these  balls  be  electrified  by  the  electricity  from  the  glass 
rod  and  the  other  from  the  sealing-wax,  they  then  mutually  attract  each 
other. 

The  same  fact  may  be  shown  by  the  gold  leaf  electroscope. 
Either  glass  or  wax,  when  excited,  will  cause  the  leaves  to  di- 
verge, but  when  the  leaves  are  repelled  by  one  kind,  the  other 
will  cause  them  to  collapse. 

Theory.  —  1.  The  state  produced  on  the  glass  rod  was  called 
positive  by  Franklin,  according  to  a  theory  which  he  proposed, 
that  the  body  had  more  than  its  natural  share  of  electricity  in 
it.  The  state  produced  on  the  sealing-wax,  and  upon  resinous 

What  effect  is  produced  by  electrifying  two  pith  balls  with  a  glass  rod  ? 
with  sealing-wax  ?  What  influence  will  the  two  electrified  balls  exert  upon 
each  other  ?  What  is  the  theory  of  Franklin  ? 


264  NATURAL   PHILOSOPHY. 

bodies  generally,  he  called  negative,  because  he  supposed  that 
these  bodies  had  less  than  their  natural  share  of  the  electric  fluid. 

2.  Du  Fay,  the  French  philosopher,  explained  the  phenomena 
on  the  theory  of  two  fluids,  one  excited  by  friction  of  glass  and 
other  vitreous  bodies,  the  other  by  friction  of  resinous  substances. 
The  former  kind  of  electricity  he  termed  vitreous,  corresponding  to 
Franklin's  term  positive,  the  latter  resinous,  corresponding  to  the 
negative  electricity  of  Franklin.  Philosophers  are  generally  in- 
clined to  adopt  the  latter  theory.  The  two  states  are  sometimes 
indicated  by  the  sign  +  for  positive,  and  —  for  negative  electricity. 

Electrics  are  therefore  divided  into  two  classes,  those  which 
produce  positive  or  vitreous,  and  those  which  produce  negative 
or  resinous  electricity,  though  some  bodies,  by  change  of  state,  or 
by  rubbing  them  with  different  substances,  will  pass  from  one  of 
these  classes  to  the  other. 

Thus,  when  cat's  fur  and  smooth  glass  are  rubbed  together,  the 
fur  is  positive  and  the  glass  negative  ;  but  when  glass  is  rubbed 
with  woolen  cloth,  the  glass  is  positive  and  the  cloth  negative. 
The  same  is  true  of  several  other  substances.  Thus  : 


Positive.  Negative. 

Cat's  Fur          and  Smooth  Glass. 
Smooth  Glass    "    Woolen  Cloth. 
Woolen  Cloth    "    Feathers. 
Feathers  "    Wool. 


Positive.  Negative. 

Paper  and  Silk. 

Silk  i"    Lac. 

Lac  "    Rough  Glass. 

Rough  Glass    "    Sulphur. 


Wool  '    Paper. 

The  Electrical  Machine. — Electricity  may  be  excited  in  suf- 
ficient quantities  to  exhibit  the  principal  phenomena  of  attraction 
and  repulsion  by  means  of  a  glass  rod  or  a  rod  of  sealing-wax, 
but  in  order  to  obtain  it  in  such  quantities  as  to  exhibit  its  prop- 
erties and  effects  in  a  more  striking  and  satisfactory  manner,  cer- 
tain machines  have  been  constructed,  called  Electrical  Machines. 
These  are  made  in  several  forms,  but  that  which  is  generally 
preferred  is  called  the  Plate  Machine,  Fig.  217,  which  consists 
of  a  plate  of  smooth  glass,  p,  which  is  made  to  revolve  upon  an 
axis  by  means  of  a  crank.  The  friction  is  applied  to  the  glass  by 
the  rubber  r,  which  consists  of  two  brass  plates,  lined  with  leath- 
er, and  connected  by  screws  so  as  to  press  on  each  side  of  the  glass 
plate.  An  amalgam  of  tin  and  mercury  is  spread  over  the  leath- 

What  is  the  theory  of  Du  Fay  ?  Meaning  of  positive  and  negative,  vitre- 
ous and  resinous.  How  are  electrics  divided?  Describe  the  electrical 
machine. 


ELECTRICAL    MACHINE. 


265 


d 


-  217.  er,  and  electricity  is 

generated  by  the  fric- 
tion of  the  rubber 
upon  the  glass.  In 
order  to  convey  the 
electricity  from  the 
excited  glass,  one  end 
of  a  metallic  rod, 
with  teeth  or  points, 
is  brought  near  its 
surface,  a,  and  the 
other  end  is  connect- 
ed with  the  prime 
conductor,  c.  This 
consists  of  a  hollow 
brass  cylinder  supported  upon  a  glass  pillar,  g,  which  insulates  it 
from  the  wooden  frame.  The  plate  and  rubber  are  also  insulat- 
ed by  the  glass  pillars,  g  g.  A  communication  is  made  between 
the  rubber  and  the  earth,  or  some  conductor,  by  a  brass  chain, 
which  also  connects  with  a  brass  ball,  d.  There  is  usually  a  cov- 
ering of  black  silk,  s,  which  aids  in  keeping  the  glass  free  from 
dust. 

When  the  plate  is  turned  both  kinds  of  electricity  are  produced, 
the  positive  upon  the  glass,  from  whence  it  is  taken  off  by  the 
metallic  points,  a,  and  accumulated  on  the  prime  conductor ;  the 
negative  upon  the  rubber,  from  which  it  is  conveyed  by  means 
of  the  chain  to  the  earth.  On  the  theory  of  two  fluids,  when  the 
machine  is  in  action  two  currents  of  electricity  are  established, 
the  vitreous  from  the  glass  to  the  prime  conductor,  and  the  resin- 
ous from  the  rubber  to  the  earth.  Machines  are  also  construct- 
ed in  which  the  glass  is  in  the  form  of  a  cylinder.  Of  late,  an 
insulated  steam-boiler  has  been  employed  for  the  purpose  of  gen- 
erating electricity,  the  steam  at  a  high  temperature  being  allow- 
ed to  flow  through  a  tube. 

Electrophorus. — The  electrophorus  may  be 
employed  for  many  purposes  for  which  the  ma- 
chine is  used*  and  is  much  less  expensive. 

It  consists  of  a  disc  of  resin,  b,  Fig.  218,  made 
very  smooth,  upon  which  electricity  may  be  de- 
veloped by  a  woolen  or  silk  cloth,  and  a  metallic 
conductor,  a,  which  is  also  a  flat  disc,  insulated 

Describe  the  plate  electrical  machine — the  electrophorus,  and  the  manner 
of  charging  it. 


266  NATURAL    PHILOSOPHY. 

by  the  glass  handle,  c.  When  the  resin  is  excited  by  friction,  the 
disc  a  is  placed  upon  it,  and  the  finger  is  applied  to  the  knob  on  a, 
to  allow  the  two  electricities  to  be  separated ;  the  plate  is  then 
lifted,  and  is  charged  with  electricity,  which  may  be  communi- 
cated as  from  the  conductor  of  the  electrical  machine. 

IV.  Property  of  the  Electric  Fluids, — 1.  The  most  generic 
property  of  electricity,  the  only  property  of  it  when  considered  as 
a  fluid,  is  that  one  kind  repels  its  own  and  attracts  the  opposite 
kind.  Bodies  electrified  with  opposite  kinds  of  electricity  attract 
each  other,  and  then,  becoming  electrified  with  like  kinds,  repel 
each  other.  That  is,  two  bodies  electrified,  the  one  by  positive, 
the  other  by  negative  electricity,  mutually  attract  each  other ; 
and  two  bodies,  when  both  are  at  the  same  time  electrified  by 
the  same  kind  of  electricity,  mutually  repel  each  other. 

Whatever  be  the  nature  of  electricity,  whether  there  be  two 
fluids  or  one,  or  whether  there  are  no  fluids,  bat  a  polarization  of 
the  molecules  of  matter,  or  whether  electricity,  like  light  and 
heat,  is  the  result  of  vibrations  in  some  elastic  medium,  the  fun- 
damental fact  or  property  above  stated  will  enable  us  to  explain 
its  phenomena.  To  aid  our  conceptions,  we  speak  of  electricity 
as  a  fluid,  or  two  fluids  wrhose  particles  are  mutually  self-repel- 
lent, but  each  fluid  possessed  of  a  strong  attraction  for  the  oppo- 
site kind.  With  this  generic  property,  we  proceed  to  illustrate 
and  explain  the  various  phenomena  which  this  agent  is  capable 
of  producing. 

2.  Attractions  and  repulsions  of  bodies  electrified  with  the 
same  and  with  opposite  fluids  are  shown  fig.  219. 

in  the  following  experiments  : 

Exp. — By  placing  the  two  pith  balls  upon  cj^ 
the  prime  conductor  of  the  electrical  machine,   ~~ 
and  turning  the  machine  so  that  positive  elec- 
tricity may  flow  upon  the  conductor,  the  pith 
balls  will  become  electrified  in  the  same  way, 
and  will  be  repelled  from  the  conductor  and 
from  each  other,  as  in  figure  217.     The'quad- 
rant  electrometer  will  show  this  fact,  and  indi- 
cate the  quantity  thrown  upon  the  conductor. 

Exp. — By  placing  the  strips  of  tissue  paper, 
Fig.  219,  upon  the  conductor,  the  strips,  being 

Mention  the  most  generic  property  of  the  electric  fluids.  What  experi- 
ments to  illustrate  attractions  and  reptilsions? 


INDUCTION. 


267 


Fig.  221. 


Fig.  220.  electrified  by  positive  electricity,  will  mutually 

recede. 

Exp. — The  same  fact  may  be  shown  by  a 
bunch  of  hair,  Fig.  220.  The  hair  will  rise  up 
and  stand  on  end,  owing  to  the  mutual  repulsion 
which  exists  between  the  separate  hairs. 

Exp. — A  very  pleasing  experiment  may  be 
performed  by  placing 
persons  upon  the  Insu- 
lating Stool,  which  con- 
sists of  a  mahogany  top, 
a,  with  glass  legs,  c  c, 
Fig.  221,  and  allowing 
them  to  hold  a  chain  in 
their  hands  connected  with  the  prime  conductor.  As  they  become  electri- 
fied, their  hair  will  rise  up,  and  present  the  appearance  exhibited  in  figure 
220. 

Exp. — If  some  fine  shreds  of  white  tissue  paper  be  sprinkled  upon  the 
conductor,  on  turning  the  machine  they  will  be  repelled,  and  appear  like 
flakes  of  falling  snow. 

If  now  a  chain  from  the  rubber  be  attached  to  the  prime  con- 
ductor, the  same  experiments  may  be  repeated,  deriving  the  elec- 
tricity from  the  ball  attached  to  the  rubber ;  but  the  electricity 
is  negative.  This  may  be  shown  by  electrifying  two  pith  balls, 
one  from  the  prime  conductor,  the  other  from  the  ball  attached 
to  the  .rubber. 

Hence  the  tivo  kinds  are  produced  at  the  same  time,  the  pos- 
itive on  the  glass,  the  negative  on  the  rubber. 

3.  Induction. — When  the  prime  conductor  is  electrified,  and 
pith  balls,  insulated  by  silk  threads,  are  brought  near  it,  they 
will  be  attracted,  because  they  are  electrified  by  the  opposite 
fluid ;  that  is,  the  same  fluid  is  driven  from  them,  and  the  oppo- 
site kind  induced.  This  is  called  Induction. 

To  exhibit  this  effect,  let  a,  Fig.  222,  be  the  prime  conduct- 
or, and  c  b,  d  e,  two  insulated  conductors,  arranged  as  in  figure 


In  what  state  is  the  rubber,  and  what  experiments  may  be  performed 
with  electricity  derived  from  it?  What  is  induction,  and  how  is  it  ex- 
plained ? 


268  NATURAL    PHILOSOPHY, 

222,  with  a  chain  attached  to  the  last  reaching  to  the  floor. 
When  the  prime  conductor  is  electrified  with  positive  electricity, 
the  others  will  also  be  electrified,  as  shown  by  the  pith  balls. 
The  positive  electricity  in  the  prime  conductor  will  repel  the  pos- 
itive fluid  from  the  side  of  the  conductor  b,  nearest  to  it,  to  the 
other  side,  c,  and  at  the  same  time  attract  the  negative  fluid. 
The  pith  balls  at  the  extremities  of  each  conductor  being  oppo- 
sitely electrified,  mutually  attract  each  other ;  that  is,  the  pos- 
itive electricity  on  a  will  repel  the  same  fluid  from  b,  and  attract 
the  negative.  At  c,  the  positive  fluid  will  drive  the  positive 
from  d,  and  attract  the  negative.  Hence  the  ends  of  the  insulat- 
ed conductors  will  be  electrified  by  opposite  fluids,  while  the  cen- 
ters will  be  neutral,  as  is  shown  by  the  balls  remaining  at  rest. 

It  is  evident  that  this  effect  will  always  be  produced  whenever 
either  kind  of  electricity  is  excited,  for  the  positive  will  repel  the 
positive  in  all  bodies  which  are  brought  near,  and  attract  the 
opposite  electricity. 

4.  An  electrified  body,  therefore,  always  induces  electricity  in 
surrounding  bodies,  throwing  them  into  a  state  opposite  to  itself, 
and  hence  there  will  be  an  attraction  between  them.  On  this 
principle  most  of  the  phenomena  of  electricity  may  be  explained, 
as  in  the  following  experiments.  Fig.  223. 

Exp. — Place  some  pith  balls  or  paper  images  between  two 
metallic  plates,  Fig.  223,  the  upper  one  insulated  by  a  glass  rod, 
and  connected  with  the  prime  conductor.  On  turning  the  ma- 
chine,  and  throwing  positive  electricity  upon  the  upper  plate,  the 
images  will  become  electrified  by  induction,  and  will  be  attract- 
ed  to  the  upper  plate,  where  they  will  be  charged  with  positive 
electricity,  and  repelled  to  the  lower  plate;  here  they  will  impart 
the  positive  electricity  to  the  plate,  become  again  negative,  and 
rise  up ;  they  are  thus  made  to  pass  rapidly  from  one  plate  to  the 
other,  and  hence  are  called  dancing  images. 

Exp. — Chime  of  Bells.  Suspend  the  chime  of  bells,  Fig.  224. 

Fig.  224,  to  the  prime  conductor,  with  a  chain  at- 
tached to  the  middle  bell,  and  extending  to  the  floor 
or  table.  The  outer  bells  will  become  electrified, 
and  attract  the  tongues  e  d ;  these,  being  insulated, 
will  receive  a  portion  of  the  electricity,  and  be  repell- 
ed to  the  central  bell,  to  which  they  will,  impart  it ; 
become  electrified  again,  and  attracted  to  the  outer 
bells.  They  will  thus  pass  back  and  forth,  carrying 

What  effect  has  an  electrified  body  upon  surrounding  bodies  ?  How  are 
the  experiments  with  the  dancing  images  explained  ?  chime  of  bells  ? 


FORCE    OF    ATTRACTION    AND    REPULSION.  269 

the  electricity  from  the  prime  conductor  to  the  earth,  and  ringing  the  bells 

at  each  vibration. 

Exp. — Electrical  See-Saw.  If  two  im- 
ages be  placed  on  the  ends  of  a  beam, 
Fig.  225,  balanced  on  a  glass  pillar,  and 
the  ball  a  be  electrified,  it  will  attract 
the  image  e,  and  then  repel  it;  b,  at  the 
same  time,  will  become  negative  by  in- 
duction, attract  c,  and  then  repel  it.  In 
this  way  a  see-saw  motion  will  be  kept 
up  as  long  as  the  machine  is  in  motion. 

In  many  of  the  above  experi- 
ments the  electricity  is  communicated  from  one  body  to  another, 
and  a  spark,  accompanied  by  a  sharp  report,  is  heard.  This  is 
produced  by  the  passage  of  the  electricity  through  the  air,  which 
is  a  non-conductor,  and  the  sudden  collapse  of  the  air,  which 
throws  it  into  undulations.  Thus,  when  the  hand  is  brought 
near  the  prime  conductor,  a  spark  darts  through  the  air  to  it, 
producing  a  prickly  sensation.  The  hand  becomes  electrified  by 
induction,  and  there  is  an  attraction  between  the  two  fluids  so 
great  that  they  part  the  air,  and  force  their  way  through  it  to 
form  an  equilibrium.  The  light  is  due  in  part  to  the  sudden 
compression  of  the  air,  by  which  its  latent  heat  is  developed,  and 
the  report  to  the  vibrations  produced  in  it  by  a  disturbance  of  its 
density  where  the  fluid  passes.  The  distance  to  which  a  spark 
will  force  itself  will  depend  upon  the  quantity  of  the  fluid  and 
the  state  of  the  air.  In  a  powerful  machine  the  spark  will  pass 
eight  or  twelve  inches.  This  distance  is  called  the  sphere  of 
communication.  In  the  case  of  induction,  however,  no  spark 
passes,  though  the  influence  is  felt  at  a  greater  distance,  some- 
times thirty  or  forty  feet.  This  distance  is  called  the  sphere  of 
influence. 

5.  Force  of  Attraction  and  Repulsion. — In  order  to  determ- 
ine the  force  of  attraction  and  repulsion  between  two  electrified 
bodies  at  different  distances,  Coulomb's  torsion  electrometer  may 
be  employed. 

This  instrument  consists  of  a  glass  jar,  A,  Fig.  226,  on  the 
top  of  which  is  placed  a  glass  tube,  B,  terminated  by  a  graduated 

Explain  the  electrical  see-saw — the  spark  and  report.  What  is  meant 
by  the  sphere  of  communication  ?  sphere  of  influence  ?  Describe  Cou- 
lomb's torsion  balance  electrometer. 


270 


NATURAL    PHILOSOPHY. 


Fig.  226. 


plate,  c.  In  the  center  of  this  plate  there  is  a  button,  with  an 
index,  a,  which  may  be  turned  so  as  to 
bring  the  index  to  any  part  of  the  scale  on 
the  graduated  arc.  To  the  end  of  this  but- 
ton is  attached  a  slender  thread  of  glass  or 
any  elastic  substance,  which  passes  down 
through  the  tube  B  in  to  A,  and  is  connect- 
ed with  a  horizontal  lever,  b,  terminated  by 
a  knob.  The  cylinder  has  also  a  scale  of 
degrees  applied  to  its  inner  surface,  from  0° 
to  180°.  If  now  the  end  of  the  lever  b 
be  positively  electrified,  and  the  indices  be 
placed  at  zero  on  the  two  scales,  a  small 
ball,  e,  positively  electrified,  and  brought 
near  b,  will  repel  it,  and  it  will  move  over 
the  graduated  arc  to  a  greater  or  less  dis- 
tance. Now,  by  turning  the  button,  a,  in 
the  opposite  direction,  the  thread  will  be 
twisted  until  the  force  of  torsion  is  sufficient  to  bring  the  lever 
back  to  the  point  from  which  it  was  repelled,  and  the  number  of 
degrees  necessary  to  do  this  is  called  the  angle  of  torsion.  Now 
the  force  of  torsion  is  always  proportioned  to  the  angle  of  torsion, 
and  hence  the  number  of  degrees  which  the  index  must  be  moved 
will  express  the  force  of  repulsion. 

Thus,  suppose  the  two  balls,  when  an  inch  from  each  other, 
exert  a  force  of  repulsion  represented  by  64°  on  the  scale,  if  plac- 
ed two  inches  their  repulsions  will  be  represented  by  16°,  and  at 
four  inches  but  4°.  If  we  examine  these  numbers,  we  find  that 
the  distances  1,  2,  4  are  represented  by  forces  which  are  ex- 
pressed by  64,  16,  4,  or  the  forces  are  as  the  squares  of  4,  2,  and 
1,  or  the  force  of  repulsion  is  inversely  as  the  square  of  the  dis- 
tance between  the  two  balls. 

It  is  found  by  similar  experiments  that  the  force  of  attraction 
betiveen  two  bodies  oppositely  electrified,  and  the  force  of  repul- 
sion between  two  bodies  similarly  electrified,  are  inversely  as 
the  square  of  the  distance  between  them.  The  intensity  of  the 
electric  force  may  also  be  indicated  by  the  quadrant  electrometer, 
or  by  any  two  electrified  bodies,  by  ascertaining  the  distance  at 
which  they  separate  or  are  attracted  toward  each  other. 

For  what  is  it  employed  ?  Illustrate  the  manner  of  ascertaining  the  law 
of  attraction  and  repulsion. 


DISTRIBUTION    OF    ELECTRICITY.  271 

V.  Distribution  of  Electricity  on  Conductors. — 1.  If  the  prime 
conductor  of  the  electrical  machine  be  a  perfect  sphere,  the  elec- 
tricity will  be  distributed  over  the  surface  equally,  but  if  it  be  of 
an  elongated  shape,  the  distribution  will  be  unequal,  the  intensi- 
ty increasing  toward  the  two  ends ;  and  if  one  end  be  reduced  to 
a  point,  it  will  permit  the  electricity  to  flow  off  into  the  atmos- 
phere, and  prevent  the  conductor  from  being  charged.  Hence, 
if  there  be  points  on  the  conductor,  the  electricity  will  be  dis- 
charged as  fast  as  it  is  generated ;  or  if  a  pointed  conductor,  as  a 
steel  rod  held  in  the  hand,  be  brought  near  the  prime  conductor 
when  the  machine  is  in  motion,  it  will  discharge  its  electricity. 
These  facts  are  easily  verified  by  experiment. 

The  reason  in  the  latter  case  appears  to  be,  that  the  opposite 
electricity  is  attracted  to  the  conductor  from  the  point,  silently 
passing  through  the  air,  and  the  equilibrium  is  restored  as  fast  as 
electricity  is  generated  by  the  machine. 

2.  Electricity  is  distributed  over  the  surface,  and  does  not  pen- 
etrate the  substance  of  the  conductor.  This  is  proved  by  testing 
the  inside  of  a  charged  conductor.  It  is  always  found  to  be  neu- 
tral. Hence  the  quantity  which  a  conductor  is  capable  of  con- 
taining is  dependent  upon  the  extent  of  its  surface ;  and  if  the  sur- 
face of  any  conductor  is  increased  by  making  it  into  a  hollow 
sphere,  the  quantity  of  electricity  which  it  is  capable  of  receiving 
will  be  increased,  though  its  quantity  of  matter  remain  the  same. 

Exp. — Take  some  tin  foil,  and  wind  it  around  an  insulated  conductor,  and 
electrify  it.  If  now  the  foil  be  unrolled,  the  intensity  of  its  electricity  will 
be  diminished,  because  the  same  quantity  is  spread  over  a  larger  surface. 

Coulomb  found  the  law  of  distribution  by  his  proof-plane,  which 
consisted  of  a  small  piece  of  gilt  paper,  insulated  with  a  handle 
of  lac.  By  applying  this  to  the  interior,  and  to  various  parts  of 
the  surface  of  conductors  of  different  forms,  and  testing  the  quan- 
tity of  electricity  by  an  electrometer,  the  distribution  was  found 
to  correspond  to  the  statements  above. 

Reaction  of  the  Air. — When  electricity  flows  from  points, 

How  is  electricity  distributed  over  the  surface  of  conductors  ?  What  ef- 
fect is  produced  by  points  on  or  near  the  conductor  ?  How  is  the  effect 
explained  ?  Does  electricity  penetrate  the  substance  of  conductors  ?  What 
effect  is  produced  by  electricity  flowing  from  points  ? 


272  NATURAL    PHILOSOPHY. 

the  particles  of  air  become  electrified  on  the  points  of  a  conduct- 
or, and  are  repelled.  This  reaction  will  cause  conductors,  when 
properly  arranged,  to  revolve. 

Thus,  in  the  Electrical  Tellurian,  Fig-  fig,  227. 

ure  227,  three  balls,  representing  the 
earth,  moon,  and  sun,  are  arranged  so  that 
they  can  revolve  on  supports  situated  at 
their  centers  of  gravity.  The  ends  of  the 
wires  which  connect  them  are  pointed  and 
bent  so  as  to  be  in  a  tangent  to  the  cir- 
cles in  which  they  revolve.  When  elec- 
trified, the  reaction  of  the  electrified  air  at  these  points  causes 
them  to  revolve  rapidly  in  a  direction  opposite  to  that  toward 
which  their  points  are  turned.  The  electrical  gamut  of  bells 
may  be  rung  by  causing  the  tongues  to  revolve  and  to  strike  the 
bells.  In  this  case  the  tongues  are  suspended  from  insulated 
wires,  which  revolve  by  means  of  the  reaction  of  the  air  upon 
their  points.  The  air  is  thrown  off  from  the  surface  of  the  prime 
conductor,  and  produces  what  is  called  the  aura,  or  breeze. 

VI.  Leyden  Jar. — 1.  The  doctrine  of  the  attraction  of  oppo- 
site fluids,  and  the  mutual  repulsion  existing  between  them,  is» 
most  satisfactorily  illustrated  in  the  case  of  the  Leyden  Jar. 

This  consists  of  a  glass  jar,  Fig.  228,  coated  on 
both  sides  to  within  a  few  inches  of  the  top  with  tin 
foil,  a  communication  being  made  with  the  inside 
of  the  vessel  by  means  of  a  wire  with  a  knob.  The 
inside  is  therefore  insulated  from  the  outside,  and 
the  glass  separates  the  two  conductors. 

By  bringing  the  knob  of  the  jar  to  the  prime  con- 
ductor, positive  electricity  will  flow  into  the  inside, 
repelling  through  the  glass  the  same  fluid  on  the 
exterior  coating,  and  attracting  the  opposite  fluid  in  its  stead. 
Then  the  two  opposite  fluids,  acting  through  the  glass,  tend  to 
retain  each  other  on  the  surface  ;  and  as  there  is  always  an  equal 
quantity  within  and  without  the  jar,  if  more  electricity  is  com- 
municated to  the  inside,  more  will  be  induced  on  the  outer  coat. 
Hence  a  much  greater  quantity  of  electricity  can  be  accumula- 

Describe  the  electrical  tellurian.  What  does  it  illustrate  ?  Describe  the 
Leyden  Jar.  On  what  principle  does  it  act?  Why  can  a  larger  quantity 
of  electricity  be  retained  on  the  jar? 


THE    LEYDEN    JAR.  273 

ted  than  if  the  same  surface  of  metal  were  continuous.  ,  It  will 
also  be  retained  a  mueh  longer  time,  as  these  two  fluids,  by  their 
mutual  attraction,  keep  each  other  in  contact  with  the  glass,  and 
hence  are  not  dissipated  so  readily  by  the  conducting  power  of 
the  air.  A  plate  of  glass  coated  on  the  opposite  sides  is  the  same 
in  principle  as  the  Leyden  jar.  In  this  case  the  electricities  are 
said  to  be  combined. 

Any  other  conductor,  as  water,  may  be  used  for  the  inside,  and 
the  hand  for  the  outside. 

Exp. — Thus,  take  a  glass  tumbler  half  full  of  water,  and  grasp  it  firmly 
in  the  hand.  If  now  the  water  be  electrified,  it  will  drive  away  the  same 
fluid  in  the  hand,  and  indoee  the  opposite,  and  the  tumbler  will  be  charged. 
Place  the  other  hand  in  the  water,  and  a  shock  will  be  received. 

This  is  the  experiment  which  led  to  the  discovery  of  the  Ley- 
den  jar.  An  experimenter  at  Leyden,  in  1746,  happened  to  hold 
a  tumbler  of  water  to  the  wire  connected  with  the  prime  con- 
ductor, and,  in  attempting  to  separate  the  wire,  received  a  shock. 
Those  who  first  received  the  sensation  represented  the  shock  to 
be  productive  of  effects,  of  the  most  serious  and  alarming  nature, 
but  much  of  it  was  probably  due  to  its  novelty  and  their  ex- 
cited imaginations. 

2.  Modes  of  charging  and  discharging  the  Leyden  Jar. — (1.) 
When  the  knob  of  the  Leyden  jar  is  held  near  the  prime  con- 
ductor, sparks  dart  from  the  conductor  to  the  knob,  growing  less 
and  less  brilliant  till  they  finally  cease,  when  the  jar  is  said  to 
Fig.  229.     be  charged. 

(2.)  To  discharge  the  jar,  a  bent  rod,  with  a  glass 
handle  jointed  at  a,  and  terminated  by  balls,  Fig.  229, 
is  applied,  one  ball  to  the  external  coating,  the  oth- 
er brought  near  the  knob,  which  is  connected  with  the 
inside  of  the  jar. 

As  the  two  fluids  can  now  pass  through  the  con- 
ducting rod*,  they  rush  together,  producing  a  bright 
flash  and  loud  report.  The  jar  is  then  said  to  be  dis- 
charged, though  there  generally  remains  a  slight 
charge,  which  requires  a  second  application  of  the  dis- 
charging rod  to  render  the  jar  entirely  neutral. 

How  was  the  principle  of  the  Leyden  jar  discovered  ?  Mention  the 
mode  of  charging  and  discharging  the  Leyden  jar. 

M  2 


274  NATURAL    PHILOSOPHY. 

(3.)  In  charging  the  jar,  it  is  necessary  to  connect  the  outside 
with  some  good  conductor.  It  is  generally  held  in  the  hand, 
which  allows  the  same  fluid  to  pass  from  the  coating  and  the  op- 
posite to  flow  on  ;  but  if  it  is  insulated,  Fig.  230. 
no  charge  can  be  communicated  to  it. 

Thus,  if  we  suspend  the  jar,  a,  Fig.  230, 
from  the  prime  conductor,  and  work  the 
machine,  it  will  be  found  that  it  is  not 
charged.  The  reason  is,  that  the  positive 
fluid  on  the  outside  can  not  be  driven  away 
and  the  negative  fluid  induced. 

That  the  positive  electricity  is  driven  from  the  outside  of  the 
jar  when  it  is  charged  from  the  prime  conductor,  results  from 
the  mutual  repulsion  of  the  same  fluid,  and  may  be  proved  ex- 
perimentally. 

Exp. — Thus,  take  a  second  jar,  c,  and  present  the  knob  to  the  outside 
coat  of  the  first,  insulated  as  above,  and  it  will  be  charged.  Three  or  four 
jars  may  thus  be  charged  by  connecting  them,  the  inside  of  each  with  the 
outside  of  the  other. 

(4.)  The  length  of  time  that  a  jar  will  retain  its  charge*  de- 
pends upon  the  state  of  the  air,  as  the  particles  of  the  air  in  con- 
tact with  its  surface  will  become  electrified,  and  slowly  convey 
the  electricity  away.  When  the  air  is  damp,  however,  it  be- 
comes a  much  better  conductor,  and  then  the  jar  is  quickly  dis- 
charged. Thus  the  moisture  of  the  breath  upon  the  surface  of 
the  glass  between  the  outside  coating  and  the  knob  will  soon  dis- 
charge the  jar,  because  it  forms  a  connecting  medium  by  which 
the  fluids  may  unite.  On  the  contrary,  when  the  air  is  dry,  and 
therefore  conducts  but  slowly,  a  jar  will  retain  its  charge  for  a 
long  time. 

(5.)  To  charge  the  jar  with  negative  electricity,  remove  the 
chain  from  the  rubber  to  the  prime  conductor,  and  bring  the 
knob  of  the  jar  to  the  ball  connected  with  the  rubber.  It  will 
then  be  charged  negatively,  as  may  be  shown  by  the  electrome- 
ter, or,  what  is  more  satisfactory,  by  the  following 

What  conditions  must  be  complied  with  in  charging  the  jar?  How  may 
a  second  and  third  jar  be  charged  at  the  same  time  ?  Under  what  condi- 
tions will  a  jar  lose  or  retain  its  charge  ?  How  may  a  jar  be  charged 
with  negative  electricity  ? 


THE    LEYDEN    JAR.  275 

Exp. — Charge  one  jar  from  the  prime  conductor  and  the  other  from  the 
rubber.  If  now  their  surfaces  be  connected,  and  the  discharging  rod  ap- 
plied to  the  knobs  uniting  the  inner  coatings  of  each,  they  will  be  dis- 
charged with  the  usual  results,  showing  that  the  jars  were  charged  with 
opposite  fluids. 

If,  however,  the  outer  surfaces  are  not  connected  by  some  con- 
ductor, no  discharge  will  occur ;  for  in  this  case  the  forces  are 
equal,  and  the  negative  in  one  jar  is  held  by  an  equal  quantity 
of  positive  on  the  outside,  and  the  positive  in  the  second  jar  by 
an  equal  quantity  of  negative  on  its  outer  surface.  The  force, 
therefore,  by  which  the  two  electricities  tend  to  unite  when  the 
inner  surfaces  are  in  contact,  is  exactly  counterbalanced  by  the 
separate  forces  on  their  outer  surfaces. 

(6.)  Electrical  Spider. — When  two  jars  are  charged  as  above 
and  their  outer  surfaces  connected,  they  may  be  discharged  by 
Fig.  231.  means  of  some  insulated  conductor  passing 

from  one  knob  to  the  other.  One  instrument 
by  which  this  may  be  effected  is  called  the 
Electrical  Spider,  Fig.  231,  which  consists  of 
a  piece  of  cork,  s,  made  to  resemble  a  spider, 
with  linen  threads  for  legs,  suspended  by  a  silk 
string  from  a  stand,  a,  between  the  two  knobs 
b  c.  The  spider  will  be  electrified  by  induc- 
tion, and  attracted  to  one  knob ;  then,  being 
electrified  in  the  same  way,  it  will  be  repelled, 
and  attracted  toward  the  other  jar.  By  thus  passing  back  and 
forth,  both  jars  will  be  gradually  discharged.  It  is  evident  from 
this  experiment  that  the  charge  of  a  jar  may  be  divided  into  a 
definite  number  of  parts. 

3.  We  have  seen  that  electricity  is  distributed  over  the  surface 
of  conductors  ;  but  in  the  Leyden  jar 

The  two  fluids  are  on  the  surface  of  the  glass,  and  not  on  the 
conductors. 

Exp. — To  prove  this,  take  a  jar  with  movable  coats.  Charge  it,  and  take 
out  the  inner  coat,  and  then  the  outer  one,  and  each  separately  will  be  found 
to  be  neutral ;  but,  on  returning  them  and  applying  the  discharging  rod, 
the  jar  will  be  discharged  without  any  loss  of  either  fluid. 

This  effect,  however,  results  directly  from  the  laws  of  attrac 
tion  in  opposite  fluids ;  for  when  either  coat  is  removed,  or  both  at 

Describe  the  experiment  of  two  jars,  the  one  with  -f-  and  the  other  with 
—  electricity.  Explain  the  action  of  the  electrical  spider.  Where  are  the 
two  fluids  in  a  charged  jar  ?  How  is  this  proved  ? 


276 


NATURAL    PHILOSOPHY. 


Fig.  232. 


the  same  time,  then  the  two  fluids,  from  mutual  attraction,  ap- 
proach each  other  as  near  as  possible,  and  the  coating  only  serves 
to  conduct  them  from  all  parts  of  the  two  surfaces,  and  to  allow 
them  to  ipa.ssfrom  the  surfaces  when  the  jar  is  discharged. 

The  Electrical  Sports- 
man, Fig.  232,  illustrates 
the  manner  of  charging 
and  discharging  a  jar  in 
succession.  The  condi- 
tion of  the  jar  is  shown 
by  the  pith  balls,  made  in 
the  form  of  birds.  It  con- 
sists of  a  Leyden  jar,  c, 
with  two  wires  connected 
with  the  inner  coating. 
On  one  wire  the  birds,  B, 
are  suspended  by  strings  ;  the  other  wire  is  terminated  by  a. knob, 
b.  The  outside  of  the  jar  is  connected  by  a  chain  to  the  toe,  e, 
of  a  metallic  image,  and  the  end  of  his  gun,  a,  is  brought  near  b. 
When  the  jar  is  charged,  the  birds  are  electrified  and  repelled ; 
but  after  the  jar  has  obtained  a  certain  quantity  of  electricity,  the 
attraction  between  the  two  balls  a  b,  which  represent  the  inner 
and  outer  surfaces  of  the  jar,  is  so  great,  that  the  fluids  rush  through 
the  air  with  a  loud  report;  at  the  same  instant,  the  birds  fall, 
showing  that  the  jar  is  discharged.  With  a  powerful  machine, 
the  jar  may  be  charged  and  discharged  in  rapid  succession. 

The  Miser's  Plate  acts  on  the  same  principle.  It  is  simply 
a  plate  of  glass,  coated  with  tin  foil  on  both  sides,  excepting  a 
few  inches  around  the  edge.  By  holding  the  hand  in  connection 
with  one  side,  and  laying  a  piece  of  money  on  the  other  and  elec- 
trifying it,  on  attempting  to  take  up  the  money  with  the  other 
hand  a  shock  will  be  imparted,  which  will  so  contract  the  mus- 
cles that  it  is  impossible  to  hold  it  or  take  it  from  the  plate. 

Electric  Battery. — When  several  jars 
have  both  their  outer  and  inner  surfa- 
ces connected  by  conductors,  they  con- 
stitute the  Electric  Battery,  Fig.  233. 
By  increasing  the  number  of  jars,  the 
quantity  of  electricity  accumulated  may 
become  very  great,  and  the  effects  are 

Describe  the  electrical  sportsman — the,  miser's  plate.  Of  what  does  the 
electric  battery  consist  1 


Fig.  233. 


EFFECTS    OF    ELECTRICITY.  277 

in  a  corresponding  degree  more  surprising.  A  battery  of  twelve 
one  gallon  jars  is  sufficient  for  the  ordinary  purposes  of  experi- 
menting. 

In  theory,  the  battery  is  the  same  as  a  single  jar  of  multiplied 
power,  as  all  the  inner  surfaces  are  charged  with  one  fluid,  and 
all  the  outer  with  another.  The  power  of  an  electrical  battery 
may  be  estimated  by  means  of  the  Balance  Electrometer,  Fig.  234, 
Fig.  234.  which  consists  of  a  lever,  a  b,  bal- 

anced upon  a  glass  stand  ;  d  is  a  brass 
ball  connected  with  the  outside  of  the 
jar,  and  c  a  similar  ball  connected 
with  the  inside  ;  a  is  a  slide  to  meas- 
ure the  force  of  attraction  and  repul- 
sion. When  the  jar  is  charged,  pos- 
itive electricity  is  thrown  upon  c  and 
O  a  b;  there  will  be  a  repulsion  between 
the  balls  at  c,  and  an  attraction  be- 
tween b  and  d,  which  will  tend  to  draw  b  down  upon  d,  and  dis- 
charge the  battery. 

VII.  Effects  of  Electricity.  —  Having  presented  the  funda- 
mental property  of  the  electric  fluids,  we  now  proceed  to  an  ex- 
perimental illustration  of  their  effects.  These  are  the  production 
of  light  and  heat,  the  mechanical,  chemical,  and  vital  effects. 

1  .  Electric  Light.  —  Electricity  passes  silently  through  good 
conductors,  without  any  indications  of  its  presence  ;  but  if  it  be  in- 
terrupted in  its  passage  by  some  non-conducting  or  imperfectly 
conducting  medium,  it  will  exhibit  the  phenomena  of  light.  Thus, 
in  the  various  experiments  already  noted,  whenever  air  intervenes 
between  any  two  bodies  electrified  by  opposite  fluids,  a  bright 
spark  is  emitted  as  the  two  fluids  pass  through  the  air. 

(1.)  By  a  series  of  conductors  placed  a  little  distance  apart, 
many  beautiful  illustrations  of  electric  light  may  be  exhibited. 
The  Spiral  Tube  is  constructed  on  this  principle.     It  consists 
-F^-235.  of  a   glass  tube, 


with  two  brass  balls,  and  the  inside  studded  with  small  spangles 
of  tin  foil,  placed  about  a  thirtieth  of  an  inch  apart.     When  one 

How  is  the  charge  of  the  battery  measured  ?  Describe  the  balance  elec- 
trometer. What  effects  are  produced  by  electricity  ?  Describe  the  spiral 
tube. 


278 


NATURAL    PHILOSOPHY. 


^-237. 


end  is  held  near  the  prime  conductor  and  the  other  remains  in 
the  hand,  the  electricity  will  pass  from  one  spangle  to  the  other, 
exhibiting  a  series  of  brilliant  sparks  at  each  point  of  interruption. 

The  Diamond  Jar  is  similar.  It  is  coated  on  both  sides  with 
circular  plates  of  tin  foil.  When  it  is  charging,  sparks  of  light 
pass  from  one  spangle  to  another,  and  when  it  is  discharged  the 
whole  becomes  luminous. 

Sometimes  words,  such  as  "  light,"  Fiff- 236- 

Fig.  236,  "  fire,"  and  "  Franklin," 
as  well  as  representations  of  animals, 
and  "  profiles  of  persons,  are  made  by 
disposing  the  spangles  in  these  forms  on  glass  or  varnished  paper." 

'(2.)  The  length  of  the  spark,  its  form  and  color,  will  depend 
upon  the  density  and  rarity  of  the  air,  and  the  nature  of  the  con- 
ductors which  give  and  receive  it.  If  the  air  is  condensed,  the 
light  will  be  white,  and  the  spark  shorter  than  at  its  ordinary 
density. 

Thus,  take  a  globe,  double  necked,  and  mounted 
with  caps,  with  a  sliding  rod,  s  a,  Fig.  237,  passing 
through  one  end,  and  a  tube,  terminated  with  a  ball, 
b,  and  stop-cock,  d,  attached  to  the  other.  The  globe 
is  air  tight,  and  the  sliding  rod,  s,  can  be  raised  or  low- 
ered so  that  the  balls  a  b  may  be  made  to  stand  at  any 
distance  from  each  other. 

By  means  of  a  condensing  pump,  a  quantity  of  air 
may  be  forced  into  the  globe,  and  charges  of  electricity 
from  the  battery  sent  through  the  air.  It  is  found 
that,  the  more  dense  the  air,  the  nearer  the  balls  must  be  placed 
in  order  that  the  spark  may  penetrate  it.  Its  course  is  also  zig- 
zag ;  but  the  rarer  the  air,  the  longer  will  be  the  spark  ;  thus  : 

Exp. — By  exhausting  the  air  from  the  globe,  the  balls  may  be  removed 
further  and  further  apart,  but  the  brilliancy  of  the  spark  is  constantly  di- 
minished, and  its  color  becomes  of  a  bluish  tint. 

The  Aurora  Tube,  Fig.  238,  will  exhibit  this  effect  in  the 
most  satisfactory  maimer.  Fig.  238. 

It  is  similar  to  the  globe,     ft       f         ;d2HU-n 

but  longer,  and  one  of  its  ^QflP-CZ ^ £Q     JUr"^ 

Describe  the  diamond  jar.  On  what  principle  is  it  that  the  spangles 
emit  sparks  of  light  ?  Upon  what  does  the  length  of  the  spark  depend  ? 
its  color?  How  is  this  proved ?  Describe  the  Aurora  tube. 


COLOR    OF    ELECTRICAL    LIGHT.  279 

caps  is  terminated  with  a  point,  a.  After  exhausting,  and  elec- 
trifying the  ball  c,  streams  of  light  pass  from  it  to  the  wire  a, 
which  must  communicate  with  a  conductor,  exhibiting  the  ap- 
pearance of  the  northern  lights.  Electricity  may  also  be  passed 
through  the  tube  from  b. 

Exp. — The  tall  receiver  may  be  used  by  sticking  several  pins  through  a 
card,  putting  it  on  the  plate  of  the  pump,  and  placing  the  receiver  over  it. 
Attaching  a  ball  to  the  sliding  rod,  on  exhaustion  the  receiver  becomes 
filled  with  fine  streams  of  light. 

The  more  perfect  the  vacuum,  the  less  the  intensity  of  the 
light ;  and  if  a  perfect  vacuum  could  be  produced,  it  has  been 
supposed  that  the  electricity  would  pass  through  without  any 
light  at  all. 

From  these  experiments,  it  appears  that  it  is  the  pressure  of 
the  air  which  retains  the  electricity  on  the  surface  of  conductors, 
and  keeps  the  jar  charged. 

Exp. — This  may  be  proved  directly  by  placing  a  charged  jar  in  the  re- 
ceiver of  the  air  pump,  and  exhausting  the  air.  The  electricity  passes  from 
the  inside  to  the  outside  like  a  flowing  stream  of  light,  and  the  jar  is  dis- 
charged. 

The  form  of  the  spark  from  the  positive  knob  is  that  of  a  pen- 
cil or  brush  of  light,  but  that  from  the  negative  ball  is  a  lumin- 
ous star. 

(3.)  Color  of  Light  in  different  Media. — If  into  the  vacuum 
of  the  air  pump  vapors  of  ether  or  alcohol  be  admitted,  or,  what 
is  better,  if  in  the  Torricellian  vacuum  a  drop  of  one  of  these 
liquids  be  poured,  it  will  evaporate  and  fill  the  space.  By  pass- 
ing electric  discharges  through  this  vapor,  different  colored  light 
will  be  observed.  Ether  gives  an  emerald  green  light ;  alco- 
hol, a  red  or  bluish  red.  Davy  noticed  the  fact  that  the  vapor 
of  mercury  in  the  Torricellian  vacuum,  when  the  tube  was  hot, 
exhibited  a  bright  green  color ;  cooled  to  twenty  degrees  below 
zero,  the  light  was  scarcely  visible  except  in  the  dark.  By  ad- 
mitting air,  the  color  changed  to  sea-green,  and  finally  to  blue 
and  purple.  On  making  a  more  perfect  vacuum  by  melted  tin, 
the  light,  when  the  temperature  was  below  zero,  became  yellow 
and  very  pale.  Hence  he  inferred  that  in  a  perfect  vacuum  no 

In  what  other  way  may  the  same  effect  be  produced  ?  How  does  elec- 
tricity pass  in  a  vacuum,  and  what  is  its  color  ?  How  may  the  color  of  the 
light  be  varied  by  ether  and  alcohol?  Mention  Davy's  experiments. 


280 


NATURAL   PHILOSOPHY. 


Fig.  239. 


light  would  be  produced ;  but  electricity  itself  is  believed  to  be 
capable  of  producing  light. 

Imperfect  conductors,  such  as  eggs,  sugar,  and  ivory,  when 
subjected  to  the  charge  from  the  electrical  battery  or  jar,  become 
luminous,  and  exhibit  a  variety  of  colors. 

For  experiments  in  illustration  of  this  principle, 
the  Egg-stand  is  a  very  convenient  instrument,  Fig. 
239.  It  consists  of  a  glass  tube,  with  a  cap  and 
balls,  the  eggs  or  other  substances  being  placed  be- 
tween the  balls  and  in  contact  with  them. 

A  ball  of  ivory  or  an  egg  becomes  crimson  ;  loaf 
sugar,  white ;  fluor  spar,  emerald  green  ;  and  in  all 
cases,  if  the  body  is  slightly  transparent,  it  becomes 
highly  so  at  the  moment  of  the  passage  of  the  charge. 
The  structure  of  the  egg  is  thus  made  distinctly 
visible,  and  the  ivory  ball  is  also  rendered  transpar- 
ent when  placed  between  the  brass  balls.  Chalk,  pipe  clay,  an, 
apple,  or  a  lemon,  will  also  become  luminous  or  phosphorescent. 

(4.)  Cause  of  Electric  Light. — What  is  the  cause  of  the  light 
in  the  above  experiments  ?  It  is  evidently  not  wholly  produced 
by  the  fluids  themselves,  for  in  that  case  it  would  be  seen  more 
distinctly  in  the  vacuum.  It  is  most  brilliant  in  condensed  air. 
The  light,  then,  must  be  occasioned  by  the  sudden  compression 
of  the  air,  as  the  electrical  fluids  pass  through  it.  We  know 
that  light  is  produced  by  compressing  the  air  in  the  fire-syringe. 
The  zigzag  course  of  the  spark  is  due  to  the  air  being  condensed 
in  front  of  it.  The  electricity  is  deflected,  and  takes  a  path 
through  portions  contiguous,  which  are  rarer. 

Thus  it  appears  that  electrical  light  is  produced  by  the  passage 
of  electricity  through  a  resisting  medium,  and  that  the  color, 
length,  and  form  of  the  spark  depend  upon  the  nature  and  form 
of  the  conductors,  and  the  nature,  density,  or  rarity  of  the  medi- 
um through  which  it  passes ;  that  the  light  is  not  wholly  pro- 
duced by  the  electricity  itself,  but  by  the  sudden  compression  of 
air,  and,  of  course,  is  similar  to  light  produced  by  any  other  means. 

2.  Mechanical  Effects  of  Electricity . — (1.)  The  production  of 

What  is  the  effect  of  passing  electricity  through  imperfect  conductors  ? 
What  is  the  cause  of  electrical  light?  Explain  the  zigzag  course  of  the  spark. 


MECHANICAL    EFFECTS    OF    ELECTRICITY. 


281 


light  will  be  found,  when  properly  analyzed,  to  be  a  mechanical 
effect  of  the  electrical  fluids.  The  fluids  pierce  the  air  and  de- 
velop its  latent  heat,  and  light  is  the  result. 

(2.)  The  sound  or  report  is  due  to  the  same  cause.  The  air  is 
suddenly  parted,  and,  as  it  collapses,  vibrations  are  produced,  caus- 
ing the  sound.  The  greater  the  quantity  of  electricity,  the  louder 
the  report ;  hence,  in  thunder  storms,  electric  discharges  through 
the  atmosphere  produce  the  sharp  and  loud  reverberations  called 
thunder. 

When  a  charge  from  a  large  battery  is  passed  through  non- 
conductors or  imperfect  conductors,  they  are  in  some  cases  ex- 
panded, in  others  perforated  or  torn  in  pieces. 

(3.)  Fluids  are  expanded,  and  their  particles  forced  asunder. 
Take  a  tumbler  of  water,  and  place  in  it  a  syphon  tube  so  small 
Fig.  240.  at  one  enc^  ^iat  before  the  water  is  electrified  it  will  only 
drop.  Upon  electrifying  the  water,  it  will  commence 
running  in  a  stream. 

The  Electrical  Bucket,  Fig.  240,  is  on  the  same  prin- 
ciple.    It  is  a  small  metal  bucket  with  a  capillary  jet  in 
the  bottom,  which  allows  the  water  to  pass  out  drop  by 
drop.     On  electrifying  the  bucket,  the  water  will  flow 
out  in  fine  streams. 
The  Electrical  Fountain  exhibits  the  same  fact.    Take  Hiero's 
fountain,  and,  having  supported  it  on  an  insulated  stool,  electrify 
the  water,  and  the  jet  will  rise  to  a  greater  height,  and  become  di- 
vided into  a  great  number  of  minute  streams,  which  are  luminous  in 
the  dark.    A  jar  may  be  charged  by  holding  it  at  the  top  of  the  jet. 
(4.)  In  order  to  exhibit  the  mechanical  effects  upon  solid  bodies, 


Fig.  241. 


The  Universal  Discharger,  Fig. 
241 ,  may  be  used.  By  placing  any 
substance  on  the  insulated  support, 
c,  between  .the  two  metallic  rods  a  b, 
charges  of  electricity  may  be  passed 
through  it  by  connecting  the  ball  on 
a  with  the  inner,  and  that  on  b  with 
the  outer  surface  of  a  battery. 


Mention  some  of  the  mechanical  effects  of  electricity.  Describe  the  elec- 
trical bucket.  In  what  manner  may  the  effect  of  electricity  be  exhibited 
by  Hiero's  fountain  ?  Describe  the  universal  discharger. 


282  NATURAL    PHILOSOPHY. 

Exp. — Place  a  thick  card  between  the  two  balls,  and  pass  the  charge 
from  the  battery  through  it.  It  will  be  found  to  be  perforated  with  a  pro- 
jection or  bur  on  each  side,  which  is  supposed  to  prove  that  the  fluids  pass- 
ed through  in  two  directions.  By  a  powerful  charge  a  quire  of  paper  may 
be  thus  perforated. 

Exp. — Substitute  a  piece  of  glass  for  the  paper,  adapting  points  to  the 
ends  of  the  rods  in  contact  with  the  glass,  and  the  electricity  from  a  power- 
ful battery  will  force  its  way  through  the  glass.  Dry  \vood,  or  almost  any 
imperfect  conductor,  may  be  used,^.nd  perforated  in  a  similar  manner. 

Exp. — Place  some  mercury  or  oil  in  a  glass  tube,  and  send  a  charge 
lengthwise  through  it,  the  tube  will  be  broken  in  pieces. 

Exp. — The  direction  of  the  charge  when  paper  is  perforated  may  be 
shown  by  painting  a  card  on  both  sides  with  vermillion,  and  placing  the 
points  of  the  discharger,  Fig.  241,  on  each  side,  but  one  a  little  below  the 
other ;  on  discharging  a  jar  through  it,  a  black  line  will  be  found  passing 
from  the  point  connected  with  the  inside  of  the  jar  to  a  hole  perforated  op- 
posite the  point,  connected  with  the  outside  of  the  jar.  This  would  seem 
to  favor  the  idea  of  but  one  fluid. 

The  force  of  electricity  to  rend  asunder  trees  and  buildings,  as 
exemplified  in  the  case  of  lightning,  is  well  known.  These  me- 
chanical effects  of  the  two  electric  fluids  seem  to  prove  that 
they  possess  two  essential  properties  of  matter,  extension  and  im- 
penetrability, and  yet  they  are  destitute  of  gravity.  No  accumu- 
lation of  electricity  will  make  any  difference  in  the  weight  of  a 
body. 

3.  Chemical  Effects  of  Electricity. — Those  phenomena  which 
are  usually  classed  as  the  chemical  effects  of  the  electric  fluids 
are  generally  due  to  the  development  of  heat  by  mechanical  com- 
pression, and  hence  they  are  strictly  mechanical  effects. 

(1.)  By  passing  electricity  through  combustible  solids  or  liq- 
uids, they  may  be  inflamed. 

Exp. — Thus,  if  a  quantity  of  ether,  alcohol,  or  spirits  of  turpentine  in  a 
cup  be  held  near  the  prime  conductor,  so  that  a  spark  may  pass  into  it,  it 
is  instantly  inflamed. 

This  is  due  to  the  heat  developed  by  the  passage  of  the  fluids 
through  the  air,  which  produce  a  sudden  compression.  The  ex- 
periment may  be  varied  by  taking  the  spark  from  a  person  on 
the  insulating  stool,  or  by  pouring  ether  into  water,  and,  after 
electrifying  the  water,  drawing  a  spark  from  it  with  the  finger. 
In  each  case  it  will  be  inflamed.  In  the  same  way,  cotton  soaked 

Describe  the  experiment  with  a  card — with  mercury  in  a  tube.  Wirat 
properties  of  matter  do  the  electric  fluids  appear  to  manifest  in  these  ex- 
periments ?  To  what  are  the  chemical  effects  of  electricity  due  ?  Why 
does  the  electric  spark  cause  bodies  to  be  inflamed  ? 


CHEMICAL  EFFECTS  OF  ELECTRICITY. 


283 


in  ether  or  spirits  of  turpentine,  and  dusted  with  resin,  may  be 
inflamed.  If  the  cotton  is  placed  on  two  balls  in  the  interior  of 
a  tin  fire-house,  and  a  charge  from  the  battery  sent  through  it,  it 
will  represent  the  appearance  of  a  house  on  fire. 

(2.)  Gases  are  ignited  and  made  to  combine  by  the  passage 
of  the  electric  fluids  through  them. 

Exp.  —  Pass  a  spark  through  a  jet  of  hydrogen  gas,  and  it  will  be  instantly 
inflamed.  But  the  most  striking  illustration  of  this  fact  may  be  made  with 
explosive  gases. 

The  Electrical  Pistol,  Fig.  242,  when  filled 
with  a  mixture  of  two  parts  of  hydrogen  and  one  of 


jz^r.242. 


T^X    oxygen,  may  be  fired  with  a  single  jar,  producing 
y    \  a  loud  report.     The  pistol  may  be  filled  by  al- 
V— '   lowing  a  jet  of  hydrogen  to  pass  into  it  from  the 
Fig.  243.  hydrogen   generator,    a  small  quantity 

mixed  with  the  air  being  explosive. 

The  Thunder  House,  Fig.  243,  is  a 
model  of  a  dwelling-house,  the  sides  mov- 
ing on  hinges,  and  the  whole  held  to- 
gether by  magnets.  In  the  interior  is  a 
brass  pistol,  which  may  be  filled  with 
explosive  gases,  and  when  these  are  ex- 
ploded the  house  is  blown  to  pieces. 

(3.)  In  all  these  cases  the  heat  is  de- 
rived from  that  contained  in  the  gases,  and  is  pressed  out  by  the 
compressing  force  of  the  electrical  fluids,  or  the  particles  of  the 
gases  are  brought  so  near  to  each  other  by  this  compression  that 
the  chemical  force  becomes  active,  and  they  unite  and  form 
water. 

When  the  electric  fluids  are  passed  through  some  solid  and 
liquid  bodies,  they  often  decompose  them,  or  cause  them  to  com- 
bine with  other  bodies.  Thus  solid  wires  of  lead,  tin,  and  iron  are 
melted  and  oxidized  by  a  charge  from  the  battery.  Gunpowder 
may  be  ignited  by  passing  a  charge  through  it.  On  the  other 
hand,  if  the  oxides  of  these  metals,  as  the  oxide  of  lead,  for  in- 
stance, be  placed  in  a  tube  and  a  charge  passed  through  them, 
they  are  reduced  to  the  metallic  state. 

How  are  gases  ignited,  and  why?  Describe  the  electrical  pistol — thun- 
der house.  Explain  these  effects.  What  substances  are  decomposed  by 
electricity  ?  • 


284  NATURAL    PHILOSOPHY. 

By  passing  electric  charges  through  water  and  some  other  liq- 
uids, they  are  decomposed  into  their  elements.  Electric  dis- 
charges through  air  cause  its  oxygen  and  nitrogen  to  combine, 
and  form  nitric  acid.  Lightning  thus  forms  nitric  acid  in  the 
atmosphere,  which  is  brought  down  by  rains,  and,  when  it  falls 
on  limestone  rocks,  produces  nitrate  of  lime,  a  substance  from 
which,  by  the  addition  of  potash,  nitre  is  obtained.  • 

In  the  case  of  decomposition,  the  action  is  different  from  that 
in  which  the  heat  of  the  air  is  developed  to  produce  combustion. 
Electricity  developed  by  chemical  action  is  one  of  the  most. pow- 
erful decomposing  agents  which  we  are  able  to  employ. 

5.  Vital  Effects  of  Electricity. — The  vital  effects  of  electrici- 
ty are  the  most  remarkable  of  any  which  this  agent  is  capable 
of  producing.  We  have  already  noticed  the  fact  that  when  the 
hand  is  held  near  the  prime  conductor  of  the  electrical  machine, 
it  gives  and  receives  a  spark,  and  this  phenomenon  is  accompanied 
with  a  slight  sensation  of  pain,  like  that  caused  by  the  prick  of  a 
pin.  And  when  a  larger  quantity,  as  the  contents  of  a  Leyden 
jar,  are  sent  through  the  system,  it  is  followed  by  a  sudden  con- 
traction of  the  muscles  of  the  arms,  and  sometimes  of  the  breast, 
producing  what  is  called  the  Electric  Shock.  This  shock  may 
be  received  through  any  part  of  the  system  by  making  it  the  me- 
dium of  communication  between  the  outer  and  inner  coats  of  a 
Leyden  jar. 

In  order  to  receive  the  shock,  two  brass  rods  may  be  held  in 
the  hands,  and  one  applied  to  the  coating  and  the  other  to  the 
knob.  Any  number  of  persons  may  receive  the  shock  at  the 
same  time  by  taking  hold  of  each  other's  hands,  thus  establishing 
a  communication,  the  individual  at  one  end  applying  the  brass 
rod  to  the  outer  coating,  and  the  one  at  the  other  end  to  the  knob 
of  the  jar. 

When  it  is  required  to  pass  the  charge  through  any  particular 
part  of  the  body,  brass  chains,  connected  with  the  inner  and  out- 
er surfaces  of  a  jar,  may  be  attached  to  two  brass  balls  with  glass 
handles,  ,and  the  balls  applied  directly  to  the  part.  A  shock 

How  does  the  action  of  electricity  differ  in  cases  of  decomposition  ? 
What  is  the  electric  shock,  and  how  may  it  be  received  ? 


VITAL    EFFECTS    OF    ELECTRICITY.  285 

passed  through  the  diaphragm  will  produce  a  shout  of  laughter, 
due  to  the  sudden  contraction  of  the  muscles. 

The  effect  of  electrical  shocks  upon  the  system  is  generally  ben- 
eficial. If  not  too  severe,  they  excite  and  stimulate  the  vital 
powers,  and  have  a  tendency  to  restore  sensation  to  any  part  that 
is  paralyzed,  or  torpid  in  its  action.  Hence  the  use  of  electricity 
as  a  remedy  for  many  diseased  states  of  the  system,  or  of  any  par- 
ticular organ.  It  promotes  perspiration,  and  quickens  the  circu- 
lation of  the  bodily  fluids.  In  cases  of  paralysis,  rheumatism,  and 
nervous  debility,  it  has  often  proved  highly  beneficial.  For  the 
purpose  of  administering  it  as  a  remedy  in  any  case,  the  shock 
may  be  varied  to  any  desirable  degree,  or  it  may  be  received  grad- 
ually into  the  system.  To  apply  it,  for  example,  to  a  nerve  of 
the  eye,  a  person  may  stand  on  an  insulating  stool,  and,  being 
charged  from  the  electrical  machine,  a  needle  may  be  applied 
near  the  eye,  and  the  electricity  drawn  off  at  that  point. 

If,  however,  a  charge  from  a  powerful  battery  be  sent  through 
any  vital  part,  serious  effects  may  be  experienced,  and  a  very 
powerful  charge  through  the  heart  or  head  would  destroy  life. 
In  experiments  upon  animals,  by  powerful  charges  life  has  been 
instantly  destroyed.  Thus  Doctor  Van  Marum  passed  electric 
charges  through  some  eels — fish  so  tenacious  of  life  that,  after 
being  cut  up  into  small  pieces,  they  exhibit  signs  of  vitality — and 
when  the  charge  passed  through  the  animals  lengthwise,  the  re- 
sult was  death,  and  the  sensation  was  destroyed  in  any  part 
through  which  a  charge  was  sent.  There  is,  therefore,  danger 
in  taking  too  severe  a  shock ;  the  result  may  be  injurious,  or  even 
fatal.  In  the  hands  of  a  skillful  physician,  however,  electricity 
is  a  most  useful  remedy  for  many  diseases.  At  the  present  time 
voltaic  electricity  is  usually  employed  for  medicinal  purposes.  In 
certain  diseased  states  of  the  system,  the  human  body  has  the 
power  of  imparting  the  electric  spark.  Persons  have  been  known 
to  give,  for  several  weeks  at  a  time,  a  spark  to  those  approaching 
them.  This  appears  to  J)e  due  to  certain  changes  going  on  in 

In  what  cases  is  electricity  beneficial  to  health  ?  How  may  it  be  admin- 
istered to  the  eye?  What  danger  is  there  in  receiving  the  shock?  What 
is  the  influence  of  electricity  on  animals  ?  What  remarkable  phenomena 
have  been  exhibited  by  persons  in  certain  states  of  the  system  ? 


286  NATURAL    PHILOSOPHY. 

the  body,  which,  under  the  appropriate  conditions,  disturb  the  equi* 
librium  of  the  two  fluids,  and  thus  the  individual  becomes  elec- 
trified. 

VIII.  Electricity  of  the  Atmosphere. — The  development  of  elec- 
tricity by  natural  agencies  gives  rise  to  some  of  the  most  sublime 
and  beautiful  phenomena  in  the  natural  world.  Changes  are 
constantly  occurring  in  nature  which  develop  the  electric  fluids. 
These  changes  are,  friction  of  the  air  on  the  earth,  and  change 
of  state  in  bodies,  such  as  the  evaporation  of  water  and  conden- 
sation of  vapor  in  the  atmosphere,  variations  of  temperature  pro- 
ducing congelation  and  liquefaction,  volcanic  eruptions,  &c. 

1.  The  friction  of  the  ivind  over  the  earths  surface,  especially 
if  the  ground  is  frozen,  develops  large  quantities  of  electricity. 

The  effect  becomes  perceptible  only  when  the  air  is  dry  and 
the  weather  cold,  for  it  is  only  then  that  the  non-conducting  pow- 
er of  the  frozen  soil  will  permit  it  to  remain.  The  stimulating 
effect  of  such  air  is  in  part  due  to  the  electricity  generated. 

2.  The  evaporation  of  water  and  its  condensation  develop 
electricity  on  a  much  larger  scale. — The  atmosphere  thus  be- 
comes more  or  less  electrified  at  all  seasons.     If  a  pointed  wire 
be  elevated  a  little  distance,  and  its  lower  end  connected  with  a 
gold  leaf  electrometer,  it  will  generally  show  signs  of  electrical  ex- 
citement, and  its  intensity  is  easily  estimated.     To  obtain  elec- 
tricity from  the  upper  regions  of  the  atmosphere,  the  electrical 
kite  is  generally  employed,  which  is  simply  a  common  kite  with 
a  fine  metallic  wire  twisted  into  the  cord.     To  the  end  of  the 
cord  a  silk  handkerchief  should  be  attached,  and  tied  within  a 
few  inches  of  the  ground.     Some  conductor,  as  water,  or  a  brass 
ball,  may  be  placed  near.     In  this  experiment  large  quantities 
of  electricity  are  often  sent  down  the  wire,  and  if  there  is  at  the 
time  any  sudden  condensation  of  vapor,  there  is  much  danger  at- 
tending it.     The  reason  why  more  electricity  exists  in  the  upper 
regions  of  the  atmosphere  is  that  the  process  of  the  condensation 

What  are  the  causes  of  the  electricity  of  the  atmosphere  ?  What  effect 
do  the  processes  of  evaporation  and  condensation  have  upon  the  state  of  the 
atmosphere  ?  How  is  the  electricity  of  the  atmosphere  ascertained  ?  Why 
is  there  more  electricity  developed  in  the  higher  than  in  the  lower  regions 
of  the  atmosphere  ? 


ELECTRICITY    OF    THE    ATMOSPHERE.  287 

of  vapor  is  almost  constant,  or  changes  are  much  more  frequent 
there  than  in  the  lower  regions. 

Franklin  was  the  first  to  charge  an  electrical  jar  from  the 
clouds,  and  to  identify  the  agent  concerned  in  lightning  with  that 
from  the  electrical  machine,  by  showing  that  the  effects  were 
precisely  the  same.  Others  have  since  succeeded,  without  ma- 
terial injury  ;  but  Professor  Bichman,  of  Petersburg,  was  in- 
stantly killed,  in  1753,  by  a  charge  passing  down  the  wire.  This 
was  occasioned  by  the  fact  that  the  wire  was  insulated  from  the 
ground  about  eight  feet ;  and  the  fluid  rushed  from  the  wire  to 
his  head,  left  a  red  spot,  singed  his  waistbands,  burst  open 'his 
shoe,  and  passed  to  the  earth. 

3.  Thunder  Storms. — When  the  sky  is  entirely  overcast  with 
clouds,  as  in  ordinary  storms,  the  electricity  generated  by  the 
condensation  of  watery  vapor  is  disseminated  over  a  wide  space, 
and  is  not  insulated  by  the  surrounding  air.  When  the  clouds  are 
somewhat  isolated,  electricity  is  accumulated  in  greater  intensity, 
and  gives  rise  to  thunder  showers  or  thunder  storms.  It  will 
readily  be  perceived  that  an  insulated  cloud,  becoming  electrified 
positively  by  condensation  of  vapor,  will  act  by  induction  upon 
any  neighboring  cloud,  and  that  there  will  be  a  strong  attraction 
between  the  two  fluids  in  the  different  clouds.  The  two  fluids, 
therefore,  will  rush  together  through  the  air,  and  produce  the 
lightning.  They  will  separate  the  air,  and,  by  its  collapse,  thun- 
der will  be  created.  Or,  if  a  cloud  becomes  positively  electrified, 
and  passes  over  a  building  or  tree  near  the  earth,  it  will  electrify, 
by  induction,  the  object  nearest  to  it,  and  the  two  fluids  will  rush 
together  through  the  intervening  air.  In  this  case  the  object  is 
said  to  be  "  struck  by  lightning." 

Thunder  storms  are  created  in  the  same  way  as  any  other 
storm,  but  are  distinguished  by  the  accumulation  of  electricity  in 
the  higher  regions  of  the  air,  due  to  sudden  condensation  of  vapor 
in  that  region,  which  sometimes  develops  positive,  sometimes 
negative  electricity,  though  the  electricity  of  the  air  in  clear 

Who  first  proved  the  identity  of  electricity  and  lightning  ?  Is  there  any 
danger  in  the  experiment  ?  Explain  the  cause  of  thunder  storms.  Why 
does  it  not  thunder  always  when  it  rains  ?  Explain  the  manner  in  which 
lightning  strikes  objects  on  the  earth. 


288  NATURAL    PHILOSOPHY. 

weather  is  generally  positive.  Thunder  storms  occur  generally 
on  a  sudden  change  of  temperature  from  hot  to  cold,  and  are 
much  more  frequent  in  hot  climates,  rarely  extending  beyond  75° 
of  latitude.  It  is  a  common  opinion  that  thunder  is  the  cause  of 
the  rain,  as  it  generally  falls  faster  after  each  clap  is  heard ;  but 
this  is  due  to  the  fact  that  sound  travels  faster  than  the  rain- 
drops. It  is  the  formation  of  the  rain  which  produces  the  light- 
ning and  the  consequent  thunder  ;  but  sound  travels  1 120  feet  in 
a  second,  and  reaches  the  hearer  before  the  rain  reaches  the 
earth.  The  lightning,  for  a  like  reason,  appears  before  the  thun- 
der, as  light  passes  more  rapidly  than  sound.  When  the  light- 
ning is  very  near,  the  clap  is  heard  at  nearly  the  same  instant. 

4.  Means,  of  Safety  from  Lightning. — It  is  evident,  from  the 
experiment  with  the  electrical  kite,  that  if  we  could  pierce  a 
cloud  charged  with  the  electric  fluid  with  an  iron  rod,  connect- 
ed with  the  earth,  we  could  discharge  all  its  electricity ;  and  if 
the  rod  was  large  enough,  and  pointed,  the  fluid  would  pass  to 
the  earth  silently  and  quietly.     But  as  electricity  is  attracted  to 
points,  if  such  a  rod  is  placed  a  few  feet  above  a  building,  and 
connected  with  the  earth,  it  will  answer  the  same  purpose,  either 
by  discharging  the  electricity  silently,  or  by  receiving  the  light- 
ning and  conveying  it  harmlessly  to  the  earth.     Such  a  rod  is 
called  a 

5.  Lightning  Rod,  which,  if  properly  constructed,  affords  the 
most  perfect  protection  from  electric  discharges  during  thunder 
storms. 

Lightning  rods  are  generally  made  of  bars  of  wrought  iron, 
three  quarters  of  an  inch  in  diameter,  and  attached  to  each  other 
either  by  hooks  or  by  screws.  The  latter  is  the  better  mode,  as 
the  contact,  and,  consequently,  the  conduction,  are  more  perfect. 
They  are  usually  attached  to  the  chimney,  extending  six  or  eight 
feet  above  it,  and  terminating  in  three  forks,  tipped  with  silver  or 
gold  leaf,  to  prevent  corrosion.  They  are  fastened  to  the  build- 
ing by  iron  or  wooden  stays  ;  the  latter  are  preferable.  The  rod 

Where  are  thunder  storms  most  frequent?  What  is  the  cause  of  the  rain 
after  a  clap  of  thunder  ?  What  means  of  safety  from  discharges  of  electric- 
ity in  a  thunder  storm  ?  Describe  the  lightning  rod. 


LIGHTNING    ROD3.  289 

is  terminated  at  the  lower  end  by  prongs  sunk  from  four  to  six 
feet  in  the  earth.  The  depth  depends  upon  the  conducting  power 
of  the  soil.  If  the  ground  is  moist,  or  if  there  is  a  well  or  spring 
of  water,  about  four  feet  will  answer  ;  if  in  dry  sand,  a  depth  of 
six,  or  even  eight  feet  is  desirable.  Charcoal  should  be  placed 
around  the  lower  extremity  of  the  rod,  both  because  it  will  pre- 
vent corrosion,  and  also  furnish  a  good  conductor  for  the  electric 
fluid.  The  rod  should  also  be  painted  with  lamp-black. 

6.  Space  protected  by  Rods. — In  order  to  determine  how  high 
the  rod  should  be  raised  in  order  to  protect  any  number  of  build- 
ings, it  is  necessary  to  observe  the  following  principle  : 

A  rod  will  protect  a  space  in  all  directions  from  its  point  equal 
to  twice  its  height.  A  rod,  therefore,  fifty  feet  high,  will  protect 
a  space  represented  by  a  cone  with  two  hundred  feet  for  the  di- 
ameter of  its  base,  extending  at  least  to  the  top  of  the  rod  fifty 
feet  in  height. 

7.  When  buildings  are  not  protected  by  lightning  rods,  the 
next  best  protection  is  for  a  person  to  stand  in  the  middle  of  the 
room  on  some  non-conducting  substance,  as  a  feather  bed.     'It  is 
more  dangerous  to  be  near  the  fire-place,  as  the  smoke  forms  a 
connecting  medium  for  the  lightning  to  descend  ;  neither  should 
a  position  be  taken  near  a  current  of  air,  as  at  a  door  or  window, 
because  the  fluid  is  liable  to  traverse  the  large  timbers,  and  may 
pass  to  the  body,  as  it  is  a  better  conductor. 

8.  When  electricity  passes  from  the  clouds  to  the  earth,  it 
will  generally  take  the  nearest  and  best  conductors.     High  ob- 
jects, such  as  church  steeples,  trees,  and  mountains,  are  most  ex- 


By  holding  a  metallic  rod  in  the  hand,  a  jar  may  be  discharg- 
ed without  passing  its  electricity  through  the  hand,  as  the  brass 
is  a  better  conductor.  But  there  are  some  exceptions  to  this 
rule.  The  fluid  will  sometimes  leave  a  good  conductor,  and  pass 
by  a  nearer  route  to  some  other  good  conductor,  through  the  air 
or  other  resisting  medium.  It  sometimes  happens,  therefore, 

How  should  the  rod  be  fitted  to  a  building  ?  How  much  space  will  a 
rod  protect  1  What  part  of  the  room  is  most  safe  in  a  thunder  storm  ? 
What  course  will  electricity  take  when  it  passes  from  the  clouds  to  the 
earth  ? 

N 


290  NATURAL    PHILOSOPHY. 

that  the  fluid  will  leave  the  timbers  of  a  house,  and  pass  directl 
across  a  room  to  some  better  conductor  on  the  opposite  side. 
Hence  the  only  real  safety  is  in  the  lightning  rod.  It  will  also 
be  noticed  that  it  is  not  safe  to  take  shelter  under  a  tree  in  a 
thunder  storm,  as  the  tree  is  a  better  conductor  than  the  air,  but 
not  so  good  as  the  human  body.  But  tall  trees  hear  a  building 
are  a  protection,  because  they  are  better  conductors  than  the 
building  itself.  Ships  and  steam-boats  are  rarely  struck  by  light- 
ning. The  reason  of  this  appears  to  be,  that  the  water  is  a  so 
much  better  conductor  than  the  vessel,  that  the  electricity  is  not 
deflected  from  its  course,  but  passes  directly  to  the  water.  Un- 
less, therefore,  the  vessel  happens  to  be  directly  under  the  cloud, 
it  will  not  be  struck. 

Velocity  of  Electricity. — The  passage  of  electricity  through 
good  conductors,  as  a  copper  wire,  for  any  distance  on  the  earth's 
surface,  is  apparently  instantaneous.  Recent  experiments  have 
shown,  however,  that  it  has  a  progressive  motion,  but  the  rate  is 
not  accurately  determined. 

Professor  Wheatstone,  of  London,  has  constructed  an  appara- 
tus by  which  he  has  attempted  to  ascertain  its  velocity.  The 
apparatus  consists  of  an  insulated  copper  wire,  half  a  mile  iri 
length,  extending  around  a  darkened  room,  and  so  disposed  that 
three  interruptions,  one  at  its  center,  and  one  at  each  extremity, 
are  arranged  near  each  other  in  a  horizontal  line.  By  sending 
a  charge  through  the  wire,  the  three  points  emit  a  spark  ap- 
parently at  the  same  moment,  but  by  placing  a  mirror  about  ten 
feet  distant,  the  sparks  will  be  seen  reflected  in  it. 

If  now  the  mirror  is  made  to  revolve  very  rapidly,  and  any  time 
intervenes  between  the  passage  of  the  sparks  at  the  three  points, 
it  will  be  indicated  by  their  being  thrown  out  of  a  straight  line. 
The  mirror  is  made  to  revolve  in  connection  with  a  Siren,  in 
which  the  number  of  revolutions  per  second  is  indicated  by  the  note 
or  tone  which  is  produced.  By  this  instrument  it  was  found  that 
an  angle  of  25  degrees  in  the  appearance  of  two  sparks  gave  an 
interval  not  exceeding  the  millionth  of  a  second ;  and  knowing  the 

What  is  the  danger  of  taking  shelter  under  a  tree  in  a  thunder  storm  ? 
How  was  the  velocity  of  electricity  ascertained  ? 


NATURE    OF    ELECTRICITY.  291 

velocity  of  the  mirror,  length  of  the  wire,  &c.,  Professor  Wheat- 
stone  estimated  the  velocity  to  be  288,000  miles  per  second  ;  but 
later  experiments  with  the  Magnetic  Telegraph  indicate  a  ve- 
locity of  from  16,000  to  30,000  miles  per  second. 

Nature  of  Electricity. — In  explaining  the  phenomena  of  elec- 
tricity, it  seemed  to  be  necessary  to  conceive  of  this  agent  as  a 
fluid,  or  as  two  highly  attenuated  fluids,  but  it  is  not  yet  fully 
settled  by  philosophers  whether  what  is  called  electricity  exists 
as  a  fluid  or  not. 

If  it  is  a  fluid,  we  are  obliged  to  regard  it  as  a  material  sub- 
stance, and  for  this  opinion  several  arguments  are  adduced. 

1.  Electricity  exhibits  some  of  the  properties  of  a  fluid.    These 
are,  its  accumulation  on  the  surface  of  conductors,  its  attractions 
and  repulsions,  its  passage  through  air  and  other  non-conductors 
producing  mechanical  effects.     It  thus  appears  to  be  impenetra- 
ble and  extended,  as  it  forces  a  passage  through  bodies. 

2.  The  fact  that  it  has  never  been  shown  to  possess  weight  and 
inertia  is  no  certain  proof  that  it  does  not  possess  these  proper- 
ties, for  many  bodies,  as  the  air  and  hydrogen  gas,  have  only 
within  a  short  period  been  proved  to  possess  them.     The  same 
is  true  of  many  organic  beings,  the  animalculse,  whose  existence 
is  only  made  known  by  powerful  microscopes. 

3.  Finally,  light  and  heat  are  known  to  be  due  to  an  elastic 
fluid  so  attenuated  that  it  has  not  yet  been  shown  to  possess  any 
of  the  common  properties  of  matter. 

Whether  there  are  two  fluids  or  one  is  not  very  material  to  the 
explanation  of  the  phenomena. 

There  are,  however,  some  reasons  for  believing  in  the  theory 
of  two  fluids.  The  mechanical  effects  indicate  this,  as  in  the  case 
of  passing  electricity  through  a  card,  there  is  a  burr  on  both  sides. 
There  is  also  a  difference  in  the  form  of  the  spark;  the  space  near 
the  conductor  is  most  illuminated ;  and  in  the  center,  or  where 
the  electricities  meet,  there  is  scarcely  any  appearance  of  light. 

The  supposition  of  two  fluids  accounts  better  for  all  the  facts, 
and  especially  for  the  distribution  of  electricity  over  conductors  of 

What  reasons  for  believing  that  electricity  is  a  fluid  ?  Mention  the  ar- 
guments for  the  existence  of  two  fluids. 


292  NATURAL    PHILOSOPHY. 

different  forms.     Most  electricians  incline  to  the  theory  of  two 
fluids. 

But  there  are  several  objections  to  the  opinion  that  there  is 
way  fluid  or  fluids  concerned  in  the  phenomena. 

1.  Its  velocity  is  so  great  that  it  appears  impossible  that  any 
fluid  could  pass  so  rapidly. 

2.  If  it  were,  like  other  aeriform  fluids,  elastic,  it  is  impossible 
to  account  for  the  equal  velocity  in  respect  to  every  portion  which 
a  charged  conductor  may  contain.    We  should  expect  the  first  por- 
tions that  flowed  from  any  conductor  would  move  more  rapidly 
than  the  last,  because  they  are  more  condensed.     The  views  of 
Mr.  Faraday  are  entitled  to  great  weight. 

"  In  the  long-continued  course  of  experimental  inquiry  in  which 
I  have  been  engaged,  this  general  result  has  pressed  upon  me 
constantly,  namely,  the  necessity  of  admitting  two  forces,  or  di- 
rections of  force,  combined  with  the  impossibility  of  separating 
these  forces  or  electricities  from  each  other."  He  mentions  sev- 
eral reasons  for  the  opinion  that  "  induction,  and  its  concomitant 
phenomena,  depend  upon  a  polarity  of  the  particles  of  matter.''' 

According  to  this  view,  electricity  consists  merely  in  the  polar- 
ity of  the  atoms  of  matter,  and  hence  no  transfer  of  any  thing 
takes  place.  This  idea  of  polarization  passing  like  a  wave  through 
conductors  is  now  the  prevailing  opinion  of  philosophers  in  re- 
spect to  the  nature  of  this  most  mysterious  agent. 

Dr.  Hare*  has  proposed  to  refer  electricity  to  polarization,  but 
he  has  brought  into  his  theory  an  ethereal  medium,  in  which  elec- 
tricity is  produced  in  a  manner  somewhat  analogous  to  the  pro- 
duction of  light  and  heat.  The  idea  of  an  all-pervading  ether, 
upon  the  vibrations  of  which  the  phenomena  of  light,  heat,  and 
electricity  primarily  depend,  is  beginning  to  be  embraced  by  the 
most  distinguished  philosophers  as  that  which  best  accords  with 
all  we  know  of  these  wonderful  agents. 

*  Journal  of  Science,  March  and  July,  1848. 

What  objections  to  the  theory  of  fluids?  What  is  the  most  probable 
theory? 


VOLTAIC    ELECTRICITY.  293 


SECTION  II.— VOLTAIC  ELECTRICITY,  OR  GALVANISM. 

I.  Voltaic  electricity  may  be  generated  by  contact  of  two  metals, 

II.  But  is  usually  produced  by  chemical  action.     The  instru- 
ments for  this  purpose  are  called  galvanic  batteries,  of  which 
there  are  two  kinds,  called  single  and  double  circles. 

III.  The  effects  of  this  kind  of  electricity  are  the  production 
of  light  and  heat,  and  the  decomposition  of  chemical  compounds. 
It  has  also  magnetic  and  vital  effects.      Voltaic  electricity  is 
applied  to  many  useful  purposes,  among  ivhich  are  the  processes 
of  gilding  and  electrography . 

VOLTAIC  electricity,  or  galvanism,  is  generally  considered  a 
branch  of  chemistry,  because  it  is  usually  generated  by  chemical 
action,  and  requires  an  apparatus  appropriate  to  the  laboratory. 
But  as  it  gives  rise  to  perceptible  motion,  it  is  proper  here  to  pre- 
sent a  few  of  its  fundamental  facts  and  principles.* 

I.  The  fact  which  laid  the  foundation  of  this  branch  of  elec- 
tricity was  noticed  by  Galvani  in  the  year  1789.  In  experiment- 
ing upon  the  muscles  of  a  frog,  he  noticed  that  contractions  of  the 
limb  were  produced  by  bringing  in  contact  two  metals  which 
were  already  in  contact  with  it. 

.  245.  The  experiment  may  be  made  by 

removing  the  skin  from  the  lumbar 
vertebrae  of  a  frog,  and,  having  found 
the  nerves,  a  a,  Fig.  245,  inserting 
a  silver  wire,  z,  so  that  it  may  be 
brought  into  contact  with  a  zinc 
plate  connected  with  the  limbs.  At 
each  contact  of  the  two  metals  vio- 
lent contractions  will  be  produced. 

The  electricity  thus  excited  was 
supposed  by  Galvani  to  be  generated  by  the  animal  system. 
Volta,  however,  showed  that  it  was  due  to  the  contact  of  the 

*  For  a  more  full  account  of  galvanism,  the  student  is  referred  to  Gray's 
Chemistry., 

Of  what  science  is  voltaic  electricity  usually  considered  a  branch,  and 
why  1  By  whom  and  under  what  circumstances  was  it  discovered  ?  To 
what  did  Galvani  ascribe  the  effect  ? 


294 


NATURAL    PHILOSOPHY. 


metals  ;  for  he  found  that  the  contractions  varied  when  different 
metals  were  employed,  zinc  and  silver  producing  the  greatest 
effect.  Fig.  246. 

This  fact  was  established  more  satisfactorily  by 
the  construction  of  a  pile,  called  the  Voltaic  Pile, 
which  consisted  of  alternate  plates  of  silver  and 
zinc,  with  moistened  cloth  between  them,  Fig.  246. 
On  connecting  the  two  extreme  plates,  one  gave  pos- 
itive, and  the  other  negative  electricity. 

There  was  found  to  be  a  remarkable  difference  between  elec- 
tricity thus  produced  and  that  obtained  from  the  electrical  ma- 
chine— the  voltaic  having  less  tension  or  intensity,  but  flowing 
in  a  continuous  stream,  and  appearing  to  be  generated  in  much 
greater  quantities.  It  has  been  supposed  that,  in  order  to  the 
production  of  electricity  in  this  pile,  there  must  be  a  chemical 
action  upon  the  plates,  and  that  it  was  no  proof  of  the  theory  of 
contact.  However  this  may  be,  we  have  direct  proof  of  the  pro- 
duction of  electricity  by  contact,  though  no  one  supposes  that  vol- 
taic electricity  is  always  so  produced.  Thus,  if  we  take  a  con- 
denser which  consists  of  two  metallic  discs,  with  some  non-con- 
ducting substance  between  them,  and  connect  it  with  the  gold- 
leaf  electroscope,  and  then  touch  the  upper  plate  with  a  piece  of 
zinc,  jjnd  the  lower  with  a  piece  of  copper,  both  of  which  being 
connected  with  the  earth,  on  raising  the  top  of  the  condenser  the 
leaves  of  the  electroscope  will  diverge,  showing  that  they  are 
electrified. 

Or,  if  a  zino  plate  be  secured  to  the  electro- 
scope, and  a  copper  plate  be  laid  upon  it  and 
then  removed,  the  leaves  will  diverge  with  posi- 
tive electricity. 

Bohnenberger's  electroscope  is  an  illustration 
of  the  excitement  of  electricity  by  contact,  and 
so  are  Zamboni's  dry  piles,  which  consist  of 
gold  and  zinc  leaf  pasted  on  paper,  and  then 
circular  pieces  cut  out,  and  several  thousand  of 

Mention  Volta's  theory  and  mode  of  establishing  it.  How  does  voltaic 
differ  from  common  electricity  ?  Mention  the  mode  of  producing  elec- 
tricity by  contact.  Describe  Zamboni's  piles. 


Fig.  247. 


SIMPLE    VOLTAIC    CIRCLES.  295 

them  pressed  together,  the  same  metal  being  in  the  same  direc- 
tion, a  b,  Fig.  247,  represent  two  of  these  piles,  and  as  their 
opposite  extremities  or  poles  are  always  in  opposite  states  of  excite- 
ment, if  a  light  ball,  c,  be  placed  between  them,  it  will  vibrate 
for  a  long  time.  This  was  at  first  supposed  to  be  a  case  of  per- 
petual motion.  It  is  similar  to  the  electrical  spider.  The  un- 
known cause  of  this  excitement  is  called  the  electro-motor  power, 
which  varies  in  different  bodies.  Metals  are  the  best  electro- 
motors. Zinc,  when  in  contact  with  platinum,  is  more  strongly 
charged  with  positive  electricity  than  when  in  contact  with  cop- 
per ;  and  as  the  quantity  of  electricity  varies  with  the  kinds  of 
metal  which  are  in  contact,  they  are  arranged  in  tables,  and 
called  the 

Scale  of  Tension. — The  following  substances  are  so  arranged 
that  each  preceding  substance  becomes  positive  in  contact  with 
that  which  succeeds. 


Zinc, 

Lead, 

Tin, 


Iron, 

Copper, 

Silver, 


Gold, 

Platinum, 

Charcoal. 


If  we  lay  any  three  plates  together,  as  zinc,  copper,  and  pla- 
tinum, the  electric  tension  of  the  platinum  and  zinc,  or  of  the  ex- 
treme plates,  will  be  the  same  that  it  would  be  if  they  were  in 
contact. 

The  theory  of  contact  to  generate  electricity  does  not  seem 
fully  to  account  for  its  production  by  the  galvanic  battery. 

II.  In  the  usual  mode  of  generating  voltaic  electricity,  chem- 
ical affinity  appears  to  bear  a  prominent  part,  and  we  will  now 
proceed  to  describe  the  mode  of  its  production,  in  connection  with 
the  apparatus  by  which  its  properties  and  effects  are  exhibited. 

1.  Simple  Voltaic  Circles. — A  simple  circle  consists  generally 
of  two  metals  and  a  liquid  to  act  upon  one  of  them.  The  metals 
employed  are  zinc  and  copper,  or  zinc  and  platinum,  or  silver. 

What  is  the  cause  of  electricity,  thus  produced,  called  ?  What  force  is 
usually  connected  with  the  production  of  voltaic  electricity  1  Describe  the 
simple  voltaic  circle. 


296  NATURAL    PHILOSOPHY. 

Thus,  let  a  plate  of  copper,  C,  Fig.  248, 
and  a  plate  of  zinc,  Z,  be  placed  in  water, 
containing  about  one  eighth  part  of  sul- 
phuric acid,  and  let  the  wires  attached  to 
the  two  plates  be  brought  into  contact  ; 
then  positive  electricity  will  flow  from  the 
copper  wire,  and  it  is  therefore  called  the 
positive  pole,  while  the  wire  attached  to 
the  zinc  plate  is  called  the  negative  pole.  The  electric  condition 
of  the  plates  is  indicated  in  the  figure  by  +  and  — .  The  end 
of  the  copper  plate  which  is  in  the  liquid  is  negative,  being  mark  • 
ed  by  — ,  and  the  part  out  is  positive,  or  +  •  The  reverse  is  the 
case  with  the  zinc  plate. 

The  theory  is,  that  positive  electricity  is  generated  on  the  sur- 
face of  the  zinc  plate  by  means  of  the  decomposition  of  the  wa- 
ter ;  that  it  passes  through  the  liquid  to  the  copper  plate,  and 
flows  off  at  the  copper  pole  ;  while  negative  electricity  commences 
also  on  the  surface  of  the  zinc  plate,  and  is  given  off  at  the  zino 
pole. 

The  quantity  of  electricity  will  depend  upon  the  amount  of 
surface  exposed  to  the  chemical  action  of  the  acidulated  water, 
and  as  such  batteries  possess  great  heating  powers,  they  have 
been  termed  by  Dr.  Hare  calorimotors. 

In  order  that  electricity  may  be  produced,  it  is  necessary  that 
the  liquid  acting  upon  the  plate  should  be  decomposed.  Chem- 
ical action  is,  therefore,  necessary  to  the  development  of  electricity 
in  this  form,  and  on  this  account  it  has  been  generally  supposed 
to  be  the  immediate  cause  of  its  production,  and  that  the  theory 
of  contact  is  inadequate  to  explain  the  phenomena. 

A  very  convenient  form  of  the  simple  battery  is  that  of  two 
cylinders  of  copper,  made  into  a  vessel,  so  that  a  cylinder  of  zinc 
may  be  placed  between  them.  Sulphate  of  copper  (blue  vitriol) 
is  employed  as  the  chemical  agent. 

2.  Compound  Voltaic  Circles. — A  compound  circle  consists  of 
a  series  of  simple  circles.  The  first  of  the  kind  was  made  by 
Volta,  is  called  the  Voltaic  Pile,  and  has  already  been  described. 

What  is  the  electric  condition  of  the  two  plates  ?  What  is  the  theory  of 
the  production  and  circulation  of  the  voltaic  currents  ?  Upon  what  does 
the  quantity  depend  ?  What  are  the  conditions  necessary  to  the  produc- 
tion of  currents  ?  What  is  a  compound  voltaic  circle  ? 


COMPOUND    VOLTAIC    CIRCLES. 


297 


Those  now  in  use  consist  either  of  two  metals  and  a  liquid,  or,  in 
some  forms,  of  two  metals  and  two  liquids.  Carbon  is  also  some- 
times employed  instead  of  one  of  the  metals. 

(1.)  The  copper  and  zinc  battery  consists  of  copper  plates,  sur- 
rounding plates  of  zinc,  and  insulated  from  them  by  some  non- 
conducting substance.  The  arrangement  is  to  connect,  by  strips 
of  copper,  the  copper  of  one  pair  with  the  zinc  of  the  next,  each 
pair  being  insulated,  and,  at  the  termination  of  the  series,  to  at- 
tach wires,  at  one  end,  to  the  copper  plate,  and,  at  the  other,  to 
the  zinc.  The  plates  are  then  immersed  in  dilute  sulphuric  acid. 
In  this  battery  positive  electricity  is  generated  upon  the  zinc 
plate,  to  which  the  wire  is  attached,  and  passes  through  the  liquid 
to  the  copper  plate,  thence  along  the  copper  strip  to  the  next  zinc 
plate,  and  thence,  through  the  liquid,  to  the  copper,  until  it  ar- 
rives at  the  termination,  or  last  copper  plate,  and  is  given  off  at 
the  attached  wire  or  positive  pole,  whenever  the  two  wires  are 
joined.  The  negative  current  moves  in  the  opposite  direction. 
When  the  wires  are  joined  the  circuit  is  said  to  be  closed,  and 
when  separated,  broken. 

But  the  battery  most  in  use  is  that  of  Professor  Grove,  called 
(2.)  Grove's  Battery. — This  battery  consists  of  a  series  of  pla- 
tinum and  amalgamated  zinc  plates,  which  are  excited,  the  zinc 
by  sulphuric  acid,  and  the  platinum  by  strong  nitric  acid. 

Fig.  249. 


Describe  the  copper  and  zinc  battery.  Mention  the  manner  in  which 
the  positive  current  circulates.  When  is  the  circuit  said  to  be  closed,  and 
when  broken?  Describe  Grove's  battery,  with  the  mode  of  charging  it. 

N  :?' 


298  NATURAL    PHILOSOPHY. 

The  zinc  plates  are  cast  in  the  form  of  hollow  cylinders,  a  a, 
Fig-  249,  with  shanks  or  projections,  b  b,  to  which  the  platinum 
plates  are  soldered.  Small  earthen  cups  are  placed  within  the 
zinc  cylinders,  and  these  latter  are  placed  in  glass  tumblers,  ff. 
The  plates  are  then  arranged  so  that  the  first  zinc  plate  has  its 
attached  platinum  plate  passed  into  the  earthen  cup  of  the  next 
zinc  plate,  and  this  second  into  the  third,  &c.  The  series  is  term- 
inated by  a  zinc  plate  at  one  end,  and  by  a  platinum  plate  at 
the  other,  with  wires  attached  to  each. 

This  battery  is  charged  by  putting  dilute  sulphuric  acid  (one 
eighth  add)  into  the  glass  tumblers,  to  act  upon  the  zinc,  and 
strong  nitric  acid  into  the  earthen  cups,  in  contact  with  the  pla- 
tinum plates. 

The  theory  of  the  action  of  this  battery  is,  that  water  is  de- 
composed by  the  zinc  plate,  and  electricity  generated,  which,  with 
the  hydrogen,  passes  through  the  earthen  cup  into  the  nitric 
acid.  Here  the  acid  is  decomposed,  the  hydrogen  uniting  with 
the  liberated  oxygen,  by  which  an  additional  quantity  of  electric- 
ity is  developed.  The  electricity  is  then  conducted  to  the  next 
zinc  plate,  and  the  same  process  is  repeated  to  the  end  of  the  se- 
ries, the  positive  electricity  being  given  off  at  the  platinum  pole, 
and  the  negative  at  the  zinc  pole.  This  and  some  other  forms, 
as  the  following  two,  will  keep  up  a  constant  flow  of  electricity 
for  a  long  time,  and  hence  are  called  sustaining  batteries. 

(3.)  Smees  Battery. — For  certain  purposes,  Fig.  250. 

especially  for  gilding,  the  battery  constructed 
by  Smee,  Fig.  250,  is  the  most  useful  of  any 
hitherto  described.  It  consists  of  a  silver  plate, 
covered  with  platinum,  placed  between  two 
zinc  plates.  The  liquid  used  is  dilute  sulphuric 
acid.  These  plates  may  be  arranged  as  double 
circles,  by  connecting  the  alternate  plates,  as  in 
the  copper  and  zinc  battery.  In  this  battery 
there  is  little  or  no  action,  excepting  when  the 
circuit  is  closed. 

(4.)  In  Bunseris  Battery,  carbon  cylinders  are  used  instead 

What  is  the  theory  of  the  action  of  Grove's  battery  ?  Describe  Smee's 
and  Bnnsen's  batteries. 


EFFECTS    OF    VOLTAIC    ELECTRICITY.  299 

of  platinum  or  copper,  the  charging  and  action  being  the  same 
as  in  Grove's  battery. 

III.  The  quantity  of  electricity  circulating  in  double  or  single 
voltaic  circles  is  measured  by  the  degree  of  deflection  which  it 
gives  to  a  magnetic  needle,  and  also  by  its  power  of  decomposi- 
tion.    The  simple  circles  possess  the  greater  heating  power,  and 
also  produce  a  greater  effect  upon  the  needle  ;  while  the  double 
circles  have  a  higher  tension,  and  greater  power  to  decompose 
chemical  compounds. 

The  quantity  circulating  in  a  voltaic  battery  will  depend  upon 
the  resistance  to  be  overcome  in  the  conductors,  and  the  tension, 
or  electric  force,  which  urges  the  electricity  through  them.  The 
longer  the  conducting  wires,  the  greater  the  resistance,  so  that 
the  force  of  the  current  will  be  less  as  the  wires  are  longer.  It 
has  been  found  by  experiment,  that  different  metals  do  not  con- 
duct the  currents  with  the  same  facility,  and  that  of  the  same 
wire  the  force  of  a  current  is  proportional  to  its  transverse  section, 
so  that  two  wires,  composed  of  the  same  metal,  will  oppose  equal 
resistance  if  their  lengths  are  inversely  as  their  transverse  sections. 

There  are  two  other  modes  of  generating  electricity ;  the  one 
by  heat,  called  Thermo-electricity,  and  the  other  by  a  magnet, 
called  Magneto-electricity.  These  will  be  considered  in  another 
connection. 

IV.  Effects  of  Voltaic  Electricity. — The  effects  of  voltaic  elec- 
tricity are,  in  many  respects,  identical  with  those  produced  by 
that  from  the  electrical  machine ;  but  there  are  certain  effects 
which  electricity  in  this  form  is  especially  fitted  to  produce. 
These  are  its  heating,  decomposing,  and  magnetic  effects. 

1.  The  Deflagrating  and  Heating  Poiver  of  Voltaic  Elec- 
tricity.— When  the  poles  of  a  galvanic  battery  are  connected  by 
a  small  wire,  this  wire  will  be  rendered  red-hot,  and,  in  many 
cases,  melted.  All  the  metals  are  melted  when  brought  between 
the  poles  of  a  powerful  battery,  and  if  in  thin  leaves,  will  burn 
with  a  color  peculiar  to  each.  When  charcoal  points  are  used, 

How  is  the  quantity  of  electricity  in  the  battery  estimated?  How  do 
the  simple  and  double  circles  differ  in  thj?ir  effects  ?  What  influence  have 
the  conducting  wires  ?  What  are  the  effects  of  voltaic  electricity  ?  Men- 
tion its  heating  effects. 


300 


NATURAL    PHILOSOPHY. 


the  most  intense  light  and  heat  are  produced,  sufficient  heat  1o 
melt  all  substances,  not  excepting  carbon,  which  has  recently 
yielded  to  its  power.  That  the  light  and  heat  are  not  due  to 
the  combustion  of  the  substances,  is  proved  by  the  fact  that  they 
are  produced  in  a  vacuum,  under  water,  or  in  gases  which  do  not 
unite  with  the  carbon.  They  must,  therefore,  be  generated  by 
the  electric  fluid  itself;  hence  voltaic  electricity  has  been  regarded 
by  some  as  a  union  of  light,  heat,  and  electricity. 

2,  Chemical  Effects  of  Voltaic  Electricity. — When  voltaic 
electricity  is  passed  through  compound  bodies,  it  separates  them, 
in  most  cases,  into  their  elements. 

Thus,  if  we  take  two  tubes,  o  h,  Fig.  251, 
and  fill  them  with  water,  and  then  invert 
them  over  the  poles  of  a  galvanic  battery, 
p  p,  the  poles  being  terminated  by  two  strips 
of  platinum  foil,  the  water  will  be  decom- 
posed ;  its  hydrogen  will  appear  in  the  tube 
connected  with  the  negative,  b,  and  its  oxy- 
gen in  that  connected  with  the  positive  pole, 
a,  of  the  battery.  There  will  be  found  to 
be  twice  as  much  hydrogen  in  h  as  oxygen 
in  o.  If  these  two  gases  are  put  together 
and  ignited,  water  will  again  be  formed. 

Many  other  substances  are  readily  decomposed  by  passing  vol- 
taic currents  through  them. 

Thus,  take  a  tube,  T,  Fig.  252,  and  put  into 
it  a  solution  of  Epsom  salts,  colored  with  the  in- 
fusion of  red  cabbage.  On  connecting  the  poles, 
the  salts  will'  be  decomposed,  the  acid  appear- 
ing at  the  positive  or  +>  and  the  alkali  at  the 
negative  or  —  pole.  If  the  poles  are  termina- 
ted by  platinum  foil,  the  effect  will  be  rendered 
visible  by  the  change  of  color.  The  alkali  will 
turn  the  infusion  green,  and  the  acid  will  change 
it  to  red. 

In  compounds  thus  decomposed,  the  add  always  goes  to  the 
positive,  and  the  alkali  to  the  negative  pole;  and  as  bodies  oppo- 

To  what  is  the  light  and  heat  ascribed,  and  why  ?  How  may  water  be 
decomposed  ?  Epsom  salts  ?  How  are  the  electric  states  of  the  elements 
of  these  compounds  ascertained  1 


Fig.  252. 


THEORY    OF    DECOMPOSITION.  301 

sitely  electrified  attract  each  other,  the  electric  state  of  the  oxy- 
gen in  the  case  of  water  must  be  negative,  and  that  of  the  hydro- 
gen positive  ;  and  in  the  case  of  the  salt,  the  state  of  the  acid 
must  be  negative,  and  the  alkali  positive.  These  states  are  not 
constant ;  for  the  same  substance  may  be  positive  in  one  combina- 
tion, and  negative  in  another.  Oxygen,  however,  always  assumes 
the  negative  state,  and  potassium  the  positive  state.  It  is  sup- 
posed that  the  electricities  are  neutralized  during  combination, 
and  that  the  elements  assume  different  electrical  states  when  the 
currents  circulate. 

Fig,  253.  Theory  of  Decomposition. — To  un- 

derstand how  a  compound  is  decom- 
posed, suppose  A  B,  Fig.  253,  be  sev- 
eral particles  of  water,  placed  between 
the  two  poles  of  a  battery,  +,  — . 
These  particles  are  non-electric  before 


the  current  circulates,  but  the  moment  the  poles  of  the  battery 
communicate  with  them,  the  oxygen  of  each  particle  turns  toward 
the  positive  pole,  represented  by  the  light  half,  and  the  hydrogen 
toward  the  negative  pole.  As  the  atom  of  oxygen  is  liberated 
at  the  -f-  pole,  the  next  takes  it  place,  and  the  third  takes  the 
place  of  the  second,  so  that  there  is  a  row  of  atoms  of  oxygen 
passing  from  the  negative  to  the  positive  pole,  each  one  of  which 
successively  combines  with  the  particles  of  hydrogen  which  are 
passing  off  in  the  opposite  direction. 

The  process  is  similar  in  all  cases  of  decomposition  by  galvanism. 

Gilding. — When  a  metallic  salt  is  decomposed,  the  metal  is 
precipitated  upon  the  negative  pole  of  the  battery.  In  conse- 
quence of  this,  the  baser  metals  may  be  covered  with  the  precious 
in  a  permanent  and  perfect  manner. 

Thus,  let  the  object  to  be  gilded,  after  being  made  clean,  be 
attached  to  the  negative  pole  of  the  battery  of  one  of  Smee's  cups ; 
two  cups  are  better  for  the  purpose,  a  larger  number  being  too 
powerful ;  and  then,  after  dipping  the  positive  pole,  which  should 
be  of  gold  or  silver,  into  a  solution  of  chloride  of  gold,  place  the 
article  toj>e  gilded  in  the  same  solution.  In  the  course  of  a  few 

Are  the  electric  states  of  bodies  constant?  Mention  the  theory  of  the 
decomposition  of  water  and  other  compounds.  Describe  the  process  of 
gilding — theory  of  the  change  which  takes  place. 


302  NATURAL    PHILOSOPHY. 

minutes  it  will  be  covered  with  the  purer  metal,  and  may  be  coated 
as  thickly  as  is  desirable  by  continuing  the  process.  A  bent  tube, 
represented  in  Fig.  252,  may  be  used  for  the  purpose  of  holding 
the  solution. 

This  is  the  most  perfect  process  of  gilding  hitherto  discovered. 
If  the  positive  pole  have  a  plate  of  the  metal  similar  to  that  in 
the  solution,  and  of  equal  size  with  the  object,  the  solution  will 
remain  of  constant  strength,  because  as  soon  as  the  chlorine  is 
liberated  from  the  gold,  which  becomes  attached  to  the  object,  it 
will  attack  the  positive  pole,  and  dissolve  an  equal  quantity  of 
gold,  so  as  to  keep  constantly  saturated. 

By  varying  the  process  slightly,  we  may  obtain  perfect  molds 
of  any  object  we  may  wish  to  copy.  This  process  is  called 

Electrography .  —  The    object    of  Fig.  254. 

which  a  mold  or  cast  is  desired,  sup- 
pose it  to  be  a  coin,  is  attached  to  the 
negative  pole  of  a  battery,  N,  Fig. 
254,  inserted  in  a  saturated  solution  of 
blue  vitriol.  The  positive  pole,  term- 
inated by  a  zinc  plate,  C,  is  placed  in 
dilute  sulphuric  acid,  facing  the  coin, 
but  separated  from  it  by  a  porous  par- 
tition, as  a  piece  of  bladder.  In  this 
case,  both  the  water  and  the  sulphate 
are  decomposed  ;  the  oxygen  of  the  water  combines  with  the 
zinc,  and  the  sulphuric  acid  with  the  oxide  thus  formed  ;  and  the 
hydrogen  of  the  water  unites  with  the  oxide  of  copper  which  the 
acid  leaves,  by  which  pure  metallic  copper  is  attached  to  the  ob- 
ject. This  coat,  when  it  is  sufficiently  thick,  may  be  separated, 
and  is  a  perfect  mold  of  the  coin,  every  line,  and  even  the  shades 
of  polish  being  accurately  copied.  From  this  a  cast  may  be 
formed. 

The  same  effect  may  be  produced  without  a  battery,  if  the  zinc 
is  connected  by  a  copper  wire  with  the  coin.  This  process  is  very 
useful  for  multiplying  coins  and  medallions. 

How  is  the  strength  of  the  solution  preserved  ?  How  may  molds  be 
made  from  coins,  and  what  are  the  changes  which  take  place  ? 


MAGNETIC    EFFECTS    OF    ELECTRICITY.  303 


SECTION  III.— MAGNETIC  EFFECTS  OF  ELECTRICITY.     MAGNETISM,  ELEC- 
TRO-MAGNETISM, AND  MAGNETO-ELECTRICITY. 

I.  Certain  ores  of  iron  are  naturally  magnetic.     Hardened 
steel  may  be  rendered  magnetic  in  several  ways. 

The  most  obvious  property  of  a  magnet  is  that  of  polarity  ; 
and  it  is  found  that  similar  poles  repel,  and  opposite  poles  at- 
tract each  other. 

II.  A.  current  of  voltaic  electricity  causes  the  magnetic  needle 
to  move  in  a  plane  perpendicular  to  that  in  which  the  current 
moves,  and  to  stand  at  right  angles  to  the  direction  of  the  cur- 
rent ;  and,  by  changing  the  direction  of  the  current,  rapid  revo* 
lutions  may  be  produced. 

III.  Currents  of  electricity  circulating  in  Jielices  of  insulated 
copper  wire  convert  soft  iron  and  steel  laid  within  the  coils  into 
powerful  magnets,  Jiaving  poles  depending  upon  the  direction 
of  the  positive  current ;  and  by  changing  the  polarity,  rapid 
revolutions  may  be  produced. 

IV.  Currents  of  electricity  circulating  in  an  insulated  copper 
ivire  at  the  moment  they  commence  to  flow  or  cease  flowing,  in 
duce  currents  of  electricity  in  surrounding  bodies,  called  Volta 
Electric  induction. 

•  V.  Magnets  have  the  power  of  inducing  currents  of  electricity 
which  produce  all  the  effects  of  those  from  the  galvanic  battery — 
a  subject  designated  Magneto- Electricity. 

VI.  The  theory  which  best  explains  these  phenomena  is,  that 
currents  of  electricity  are  developed  in  all  magnetic  bodies;  and 
when  two  currents  are  parallel,  and  flowing  in  the  same  direc- 
tion, they  attract,  and  when  in  opposite  directions,  they  repel 
each  other. 

VII.  Electro-magnetism  is  applied  to  several  useful  purposes, 
the  most  important  of  which  are  the  electro-magnetic  telegraph, 
and  the  magnetic  clock,  or  Electro- Chronograph. 

VIII.  Voltaic  electricity  exerts  a  powerful  effect  upon  animals. 

IX.  Some  animals  have  the  power  of  generating  the  electric 
fluid. 

IT  has  long  been  known  that  common  electricity  influences 


304  NATURAL    PHILOSOPHY. 

the  magnetic  needle.  But  the  discovery  of  Oersted  (1819)  opened 
a  new  field  of  investigation,  which  has  led  to  the  most  useful  and 
surprising  results. 

I.  Magnetism. — Magnetism  is  so  closely  allied  to  electricity, 
that  we  have  concluded  to  present  a  few  of  its  fundamental  facts 
in  this  connection. 

The  fact  that  a  magnet  will  induce  currents  of  electricity,  and 
that  these  same  currents,  as  well  as  those  from  the  battery,  will 
induce  magnetism,  shows  a  close  connection  between  them. 

1.  Magnetism  is  a  peculiar  attraction,  which  may  be  devel- 
oped in  iron  and  some  of  its  ores,  and  slightly  in  nickel  and  in 
cobalt. 

Certain  ores  of  iron  are  found  to  be  naturally  magnetic,  and 
hence  are  called  Natural  Magnets  or  Loadstones. 

But  when  the  magnetic  property  is  developed  in  a  steel  bar, 
by  artificial  processes,  it  is  called  an  Artificial  Magnet. 

When  magnetism  is  induced  in  a  bar  of  hardened  steel,  it  is 
retained,  and  is  then  called  a  Permanent  Magnet. 

Soft  iron  does  not  retain  the  magnetic  property,  though  it  may 
be  rendered  powerfully  magnetic. 

2.  Magnetism  manifests  itself  by  attractions  and  repulsions. 
The  most  obvious  property  of  a  magnet  is  that  of  polarity  ;  that  is, 

If  iron  filings  be  sprinkled  upon  a  Fig.  255. 

magnet,  Fig.  255,  they  will  adhere 
mostly  to  its  two  extremities,  d  d, 
called  its  poles,  where  the  power  ap- 
pears to  reside.  The  line  which  joins  them  is  called  its  axis. 

If  a  sheet  of  paper  be  laid  Fig.  256. 

upon  a  magnet,  and  iron  filings 
sprinkled  over  it,  they 
range  themselves  in  curves, 
in  Fig.  256.     If  a  piece 
instead  of  the  paper,  be  used, 
same   effect  will   be   produc 
The  interposed  bodies,  the 
and  the  paper,  have  no  tendency 
to  destroy  the  force  of  attraction. 

Define  magnetism.    What  are  natural  magnets  ?    What  are  artificial  mag 
nets?    How  does  magnetism  manifest  itself? 


MARINER  S    COMPASS. 


305 


Fig.  258. 


A  magnetic  needle  is  simply  a 
magnetized  piece  of  steel,  balanced 
upon  a  pivot,  Fig.  257,  so  as  to 
move  freely  in  a  horizontal  direc- 
tion When  such  a  needle  is  free 
to  move,  one  pole  always  points 
toward  the  north,  and  the  other 
toward  the  south,  and  are  called 
the  north  and  south  poles. 

A  magnetic  needle  placed  in  a  box  with  certain  fixtures  consti- 
tutes the  Land  Com- 
pass and  the  Mari- 
ner's Compass.  In 
the  latter,  the  nee- 
dle is  attached  to  a 
circular  card,  Fig. 
258,  which  is  divided 
into  thirty-two  equal 
Q  parts. 

The  box  containing 
the  needle  is  sustain- 
ed in  gimbals,  which 
consist  of  two  pairs  of 
pivots,  E  F,  p,  fixed 
in  the  circumference  of  two  rings,  at  right  angles  to  each  other, 
so  that,  whatever  the  motion  of  the  ship,  the  compass-box  main- 
tains a  horizontal  position. 

3.  The  opposite  poles  of  a  magnetic  needle  attract,  and  simi- 
lar poles  repel  each  other ;  that  is,  a  north  pole  will  attract  a 
south  pole  and  repel  a  north  pole,  or  a  south  pole  will  attract  a 
north  and  repel  a  south  pole. 

In  these  respects  the  magnetic  needle  bears  the  closest  analogy 
to  bodies  similarly  and  oppositely  electrified ;  hence  some  have 
inferred  the  existence  of  two  fluids,  the  northern  called  Boreal, 
and  the  southern  called  Austral  magnetism. 

4.  Magnetism  is  developed  by  Induction. — For  if  a  piece  of 


What  is  a  magnetic  needle  ?     Describe  the  mariner's  compass.     What  is 
the  principal  property  of  the  needle  ?     How  is  magnetism  developed  ? 


306  NATURAL    PHILOSOPHY. 

soft  iron  be  brought  near  the  poles  of  a  magnet  it  becomes  mag- 
netic, the  north  pole  of  the  permanent  magnet  inducing  a  south 
pole  on  the  end  of  the  iron  next  to  it ;  but  the  iron  loses  its  mag- 
netism when  the  magnet  is  removed.  A  hardened  steel  bar, 
when  brought  into  contact  with  a  magnet,  becomes  permanently 
magnetic. 

5.  The  two  poles  of  a  magnet  can  not  be  separated,  for  if  one 
pole  be  broken  off,  each  portion  will  immediately  assume  north 
and  south  polarity.     In  this  respect  magnetism  differs  from  elec- 
tricity, it  being  easy  to  isolate  the  two  electricities  from  each  other. 

6.  Magnetism,  however,  like  free  electricity,  resides  upon  the 
surface,  so  that  a  hollow  cylinder  of  steel  will  exhibit  magnetic 
properties  equally  powerful  with  one  which  is  solid. 

7.  The  laiv  of  magnetic  attraction  and  repulsion,  as  establish- 
ed by  Coulomb  with  his  torsion  balance  electrometer,  is,  that 
the  force  of  attraction  and  of  repulsion  between  two  magnets  is 
inversely  as  the  square  of  the  distance  between  them — the  same 
law  which  prevails  in  electricity,  light,  heat,  and  gravitation. 

8.  Magnets  may  be  produced  simply  by  taking  a  bar  of  hard- 
ened steel,  placing  the  pole  of  an  artificial  magnet  upon  it  about 
midway,  and,  inclining  it  to  an  angle  of  about  45°,  drawing  it  to- 
ward the  end.     When  this  has  been  repeated  a  few  times,  the 
steel  will  be  rendered  permanently  magnetic.    But  the  best  mode 
of  producing  powerful  magnets  is  by  voltaic  electricity. 

Magnets  are  often  made  in  the  form  of  a  horse-shoe, 
Fig.  259,  with  a  piece  of  soft  iron  placed  across  the  ends 
of  the  poles,  called  an  armature,  which  aids  in  preserving 
the  magnetic  power.  The  end  of  the  armature  next  to 
the  north  or  +  pole  has  south  or  —  polarity,  and  the 
end  in  contact  with  the  south  pole  has  +  or  north  po- 
larity. 

9.  Variation  of  the  Magnetic  Needle. — The  magnetic  needle 
stands  directly  north  and  south  in  but  a  few  places  on  the  earth's 
surface,  but  varies  to  the  east  or  west  in  different  places.    Lines 

Can  the  poles  of  a  magnet  be  isolated  ?  What  is  the  law  of  attraction 
and  repulsion  ?  How  may  a  magnet  be  produced  1  What  is  the  best  mode 
of  producing  magnets  ?  What  is  meant  by  the  variation  of  the  needle,  and 
how  does  it  vary  ? 


ELECTRO-MAGNETISM. 


307 


connecting  those  places  where  the  needle  stands  north  and  south 
are  called  lines  of  no  variation.  These  lines,  in  fact,  form  but 
one,  which  entirely  encircles  the  globe. 

There  is  a  point  in  latitude  70°  5'  north  and  longitude  96°  45' 
west,  where  the  needle  stands  vertically.  There  is  also  a  similar 
point  in  the  southern  hemisphere  at  72°  south  latitude  and  152° 
east  longitude.  There  are  also  two  points  in  the  northern  hemi- 
sphere called  points  of  maximwn  intensity.  The  stronger  is  in 
latitude  52°  19'  north  and  longitude  92°  west.  The  weaker  is 
in  latitude  85°  north  and  longitude  116°  east.  These  have  cor- 
responding points  in  the  southern  hemisphere. 

II.  Electro-magnetism. — The  fundamental  fact  noticed  by 
Oersted  was,  that  a  current  of  electricity,  circulating  in  a  copper 
wire,  or  any  other  conductor,  produced  certain  definite  motions  of 
a  magnetic  needle,  dependent  upon  the  direction  of  the  current. 

1 .  Influence  of  Voltaic  Currents  upon  the  Magnetic  Needle. — 
Fig  260  If  a  magnetic  needle  be  freely  sus- 

~  '  '.>». pended,  Fig.  260,  with  its  north 

""""•**•  pole  pointing  to  the  north,  and  a 
current  of  positive  electricity  passed 
from  north  to  south  directly  above 
it  in  a  vertical  plane,  the  north  pole 
of  the  needle  will  turn  toward  the 
east,  and  stand  in  the  direction  cd; 
or,  if  the  current  pass  under  the  nee- 
dle from  south  to  north,  the  same 
effect  will  be  produced.  By  pass- 
ing an  insulated  wire  several  times 
around  the  needle  the  effect  will 
be  increased.  An  instrument  thus 
constructed  is  called  a  Galvanom- 
eter, Fig.  261. 

But  if  the  positive  current  be  passed  from  south  to  north  above 
the  needle,  the  north  pole  will  turn  toward  the  west.  This  de- 
flection is  never  as  much  as  90°,  on  account  of  the  tendency  of 
the  needle  to  place  itself  in  a  north  and  south  direction ;  but  if 
an  astatic  needle  is  used,  that  is,  two  needles  with  their  north 

What  were  the  facts  noticed  by  Oersted?  Describe  the  galvanometer. 
What  is  the  effect  of  passing  a  positive  current  from  north  to  south  above 
the  needle  ?  Why  is  the  deflection  less  than  90°  ? 


308 


NATURAL    PHILOSOPHY. 


Wig.  262. 


and  south  poles  united,  the  deflection  will  be  90°  ;  hence  the 
tendency  of  a  magnetic  needle  is  to  stand  at  right  angles  to  the 
direction  of  a  voltaic  current,  the  needle  moving  in  a  plane  per- 
pendicular to  that  in  which  the  current  moves.  It  will  be  no- 
ticed that  this  force  acts  tangentially,  and  in  this  respect  differs 
from  any  force  hitherto  considered. 

2.  Revolutions  of  the  Needle. — When  the  needle  turns  toward 
the  east,  its  inertia  will  carry  it  past  that  point,  and  then,  if  the 
direction  of  the  current  is  changed,  its  north  pole  will  turn  to- 
ward the  west,  and  will  pass  through  the  south  point  to  reach 
it ;  if  then  the  current  is  again  changed,  it  will  complete  a  revo- 
lution, and  in  this  way  rapid  revolutions  may  be  given  to  the 
needle. 

If  the  needle  is  first  made  to  turn  to  the  west,  it  will  revolve 
in  the  opposite  direction. 

Revolutions  may  also  be  produced  by  passing  currents  of  elec- 
tricity through  the  needle  itself. 

Thus,  if  a  magnet  be  placed  upon  its 
north  pole,  Fig.  262,  and  currents  of 
positive  electricity  are  passed  through 
half  its  length,  it  will  revolve  rapidly, 
the  direction  depending  upon  the  direc- 
tion of  the  currents.  A  little  mercury 
must  be  placed  in  a  cup  at  the  center 
of  the  needle,  and  the  connection  made 
with  B  by  a  wire  which  dips  into  it. 
The  two  poles  of  the  battery  may  be 
connected  with  B  and  C,  which  will 
send  the  currents  through  the  lower 
half,  or  with  A  and  B,  which  will 
send  them  through  the  upper  half  of 
the  magnet,  S  N. 

3.  If  the  needle  is  made  stationary,  and  the  conducting  wire 
attached  to  an  axis,  it  will  revolve  rapidly,  owing  to  the  reaction 
of  the  magnet,  provided  the  current  is  sent  in  opposite  directions 
at  each  half  revolution. 

How  does  a  magnetic  needle  tend  to  stand  in  reference  to  a  voltaic 
current  ?  How  may  revolutions  be  given  to  a  needle  ?  How  may  revolu- 
tions be  produced  in  the  conducting  wire  ? 


THERMO-ELECTRICITY. 


309 


Fig.  263. 


Thus,  let  a  copper  wire,  C,  Fig. 
263,  wound  in  the  form  of  a  rect- 
angle, be  attached  to  an  axis,  and 
placed  between  the  poles  of  a  per- 
manent horse-shoe  magnet,  the  ends 
of  the  wires  being  soldered  to  two 
strips  of  silver  on  each  side  of  the 
axis,  so  that,  as  the  rectangle  re- 
volves, the  ends  may  be  brought  al- 
ternately in  contact  with  springs  of 
silver,  which  are  connected  with  p 
and  n,  and  these  with  opposite  poles 
of  a  single  battery,  Smee's  being  the 
best  for  this  purpose. 

As  the  positive  current  passes 
from  north  to  south  above  the  nee- 
dle, the  side  next  to  the  north  pole 
turns  to  the  west,  because  the  pole 
itself  can  not  turn  to  the  east,  and 
when  it  has  completed  a  quarter  of 
a  revolution,  the  other  end  of  the 
wire  receives  the  positive  fluid,  and 
the  revolution  continues  until  the  rectangle  has  passed  three  quar- 
ters of  a  revolution,  when  the  current  is  again  reversed.  It  will 
be  seen  that  the  current  is  reversed  every  half  revolution,  as  in 
the  case  of  the  magnet. 

4.  Two  conducting  wires  may  be  made  to  revolve  by  sending 
currents  through  them  in  different  directions  ;  those  positive  cur- 
rents which  flow  in  the  same  direction  will  attract,  and  those  which 
flow  in  opposite  directions  will  repel  each  other. 

If  the  conducting  wires  are  made  of  different 
metals,  as  bismuth  and  antimony,  then  the  currents 
may  be  generated  in  them  by  heat,  and  revolutions 
produced.  Electricity  thus  excited  is  termed, 

5.  Thermo-electricity. — Thus,  let  #,  Fig.  264, 
be  a  bar  of  antimony,  and  b,  of  bismuth,  soldered 
together  at  the  point  c,  and  the  other  extremities 


Fig.  264. 


How  may  revolutions  of  two  conducting  wires  be  produced  ?     Describe 
the  mode  of  exciting  currents  by  boat,  and  of  producing  revolutions. 


310 


NATURAL    PHILOSOPHY. 


Fig.  265. 


connected  by  wires.  When  the  junction,  c,  is  heated,  a  current 
of  electricity  will  flow  from  the  bismuth  to  the  antimony,  and 
when  the  junction  is  cooled,  a  current  will  flow  in  the  opposite 
direction.  The  currents  are  feeble,  but  may  be  increased  by 
uniting  a  series  of  bars,  as  in  the  compound  voltaic  circles.  The 
existence  of  these  currents  may  be  shown  by, 

6.  Thermo-electric  Arches. — Figure  265 
represents  two  arches,  s  s,  placed  on  the 
poles  of  a  permanent  magnet.  Each  consists 
of  rectangular  wires  of  silver,  soldered  to  a 
circular  wire  of  German  silver.  When  the 
junctions  are  heated,  currents  of  electricity 
flow  from  the  German  silver  to  the  silver, 
passing  up  the  heated  side  of  the  arch  and 
descending  the  other  side.  These  currents 
give  polarity  to  the  rectangle,  and,  by  the 
influence  of  the  pole  of  the  magnet,  the  arch 
revolves,  bringing  the  junctions  successively 
into  the  flame,  by  which  the  direction  of  the 
current  is  changed  in  each  rectangle  every 
half  revolution.  The  principle  is  the  same 
as  in  the  revolving  rectangle. 

III.  Influence  of  Voltaic  Currents  on  Soft  Iron  and  Steel. 

1.  If  a  bar  of  soft  iron  be  inserted  in  a  coil  of  insulated  copper 
wire,  and  the  two  ends  of  the  wire  connected  with  the  poles  of  a 
simple  voltaic  circle,  it  will  be  instantly  converted  into  a  magnet, 
but  will  lose  its  magnetism  when  the  circuit  is  broken  ;  but  if  the 
bar  is  hardened  steel,  it  will  be  ren- 
dered permanently  magnetic. 

Thus,  let  C,  Fig.  266,  be  a  coil 
of  wire,  called  a  helix,  and  N  S  a 
bar  of  iron  or  steel"  inserted  in  it. 
The  poles  of  a  battery,  n  p,  may 
be  attached  by  means  of  the  cups 
which  are  in  connection  with  the 
ends  of  the  wire  constituting  the 
coil.  While  the  currents  are  cir- 
culating, small  nails  or  keys  will 
be  strongly  attached  to  the  two 
poles. 

What  is  the  effect  of  currents  of  electricity  on  soft  iron,  and  how  may  it 
be  exhibited  ?  what  upon  steel  ? 


Fig.  266. 


ELECTRO-MAGNETS. 


311 


• 267<  If  the  soft  iron  is  made  in  the  form  of 

two  semicircles,  Fig.  267,  with  handles 
attached,  and  placed  within  the  coil,  c, 
they  will  be  held  together  with  great 
force  when  the  two  ends  of  the  wire,  P 
N,  are  connected  with  a  battery,  but 
are  easily  separated  when  the  circuit  is 
broken.  If  the  heliacal  ring,  c,  is  made 
with  a  small  opening,  it  will  cause  small 
nails  to  adhere  to  it  while  the  current 
is  circulating,  but  as  soon  as  the  circuit 
is  broken  the  nails  will  fall. 

The  same  effect  will  be  produced  if  the  wire  is  wound  around 
the  iron  in  the  manner  represented  in  Fig.  268.     In  this  case  it 

1^.268. 


is  called  an  Electro-magnet.  An  armature,  connected  with  a 
steel-yard,  being  applied,  the  force  of  attraction  is  easily  determ- 
ined. The  longer  the  wire  within  certain  limits,  the  greater  the 
effect. 

Professor  Henry,  to  whom  we  are  indebted  for  many  experi- 
ments on  this  subject,  first  succeeded  in  making  electro-magnets 
which  would  sustain  1000,  2000,  and  even  3000  pounds. 

When  pieces  of  hardened  steel  are  drawn  across  the  poles  of  an 
electro-magnet,  we  may  obtain  more  powerful  permanent  mag- 
nets than  by  any  other  process. 

2.  The  poles  of  the  magnet  in  these  experiments  depend  upon 
the  direction  in  which  the  currents  circulate. 


What  is  an  electro-magnet  ? 
pend? 


Upon  what  do  the  poles  of  the  magnet  de- 


312 


NATURAL    PHILOSOPHY. 


Thus,  if  we  take  a  coil  of  wire,  represented  in  Fig.  266,  place 
within  it  a  bar  of  soft  iron,  the  bar  standing  north  and  south,  and 
then  pass  a  current  from  the  copper  or  positive  pole  of  the  battery 
around  the  bar  from  north  to  south,  in  a  direction  opposite  to 
that  in  which  the  sun  appears  to  move,  the  north  end  of  the  bar 
will  be  a  north  pole  and  the  south  end  a  south  pole,  as  may  be 
shown  by  its  attracting  the  opposite  poles  of  the  magnetic  needle. 
But  if  the  positive  current  circulate  in  the  same  direction  in 
which  the  sun  appears  to  move,  the  south  end  will  be  the  north 
pole,  and  the  north  end  the  south  pole  of  the  needle. 

3.  Revolutions  of  Electro-magnets. — If  by  any  means  we  can 
change  the  direction  of  these  currents,  so  as  to  change  the  polar- 
ity of  the  iron  bar,  we  may  produce  rapid  revolutions.  For  this 
purpose,  the  bar  is  wound  with  insulated  copper  wire,  and  affixed 
to  an  axis  between  two  poles  of  a  per-  Fig.  269. 

manent  hwse-shoe  magnet,  or  of  an- 
other electro-magnet.  This  is  the  prin- 
ciple of 

Page's  Revolving  Magnet. — It  con- 
sists of  a  small  electro-magnet,  a,  Fig. 
269,  fix*ed'to  an  axis,  s,  upon  two  sides 
of  which,  near  the  lower  extremity,  are 
two  pieces  -of  silver,  extending  nearly 
around  the  axis,  to  which  the  two  ends 
of  the  wire  surrounding  a  are  soldered. 
Two  springs  of  silver,  connected  with 
the  two  cups,  p  r,  press  on  each  side 
of  the  axis  in  contact  with  the  strips 
of  silver.  As  these  do  not  extend  quite 
around  the  axis,  there  are  two  spaces 
which  constitute  a  break,  so  that  op- 
posite ends  of  the  wire  receive  the  cur- 
rent as  the  axis  revolves,  and  by  this 
means  the  polarity  is  reversed  at  each 
half  revolution. 

The  operation  of  this  instrument  depends  upon  the  fact  that 
opposite  poles  attract  and  the  same  poles  repel  each  other. 

By  the  direction  of  the  currents,  two  north  and  two  south  poles 
are  made  adjacent  to  each  other,  and  there  will  be  a  mutual  re- 


Describe  Page's  revolving  magnet.     How  are  the  revolutions  produced  ? 


VOLTA-ELECTRIC    INDUCTION.  313 

pulsion.  The  electro-magnet  will  be  repelled  one  quarter  of  a 
revolution,  and  then,  because  opposite  poles  attract,  will  be  at- 
tracted one  quarter  of  a  revolution  further.  At  this  point  the 
poles  are  reversed,  and  the  repulsions  and  attractions  continue. 

The  rapidity  of  these  revolutions  is  very  remarkable.  The 
poles  are  changed  every  half  revolution,  and  yet  instruments  have 
been  known  to  revolve  more  than  6000  times  in  a  minute.  To 
accomplish  this,  the  current  must  pass  through  some  30  feet  of 
wire  twice  each  revolution. 

In  order  to  measure  the  number  of  revolutions,  a  bell,  b,  is  at- 
tached to  this  instrument,  with  a  wheel,  which  is  turned  by  an 
endless  screw  upon  the  axis,  so  that  for  every  100  revolutions  the 
bell  strikes. 

Many  attempts  have  been  made  to  apply  this  power  to  the 
propelling  of  machinery,  and  small  engines  have  been  constructed, 
but,  as  yet,  without  much  success. 

4.  The  attracting  power,  in  case  of  electro-magnets,  is  not 
confined  to  the  iron,  but  the  conducting  wire  itself  has  the  power 
of  attracting  iron  filings. 

Nor  does  the  attraction  exist  alone  between  tbe  magnets  or 
iron  and  the  wire,  but  also  between  two  wires  conveying  a  cur- 
rent in  the  same  direction.  Thus,  when  a  coil  of  wire  has  cur- 
rents of  electricity  sent  through  it,  the  separate  coils  will  approach 
each  other  and  render  the  coil  shorter  ;  hence, 

5.  Two  currents  ivhichfloiu  parallel  and  in  the  same  direction 
attract  each  other,  but  if  they  jlow  in  opposite  directions  they 
repel  each  other,  and  from  two  such  currents  circulating  in  con- 
ducting wires  we  may  produce  all  the  attractions  and  repulsions 
exhibited  by  magnets. 

IV.  Volta-electric  Induction. — Voltaic,  like  common  electrici- 
ty, has  the  power  of  inducing  electricity  in  surrounding  bodies ; 
but  lor  this  purpose  a  special  apparatus  is  required. 

1  If  an  insulated  copper  wire  be  wound  around  an  electro- 
magnet, or  around  another  coil  of  wire,  and  the  inner  coil  be  con- 
By  what  means  is  the  velocity  of  revolutions  determined?  On  what 
principle  is  it  that  the  attractions  and  repulsions  exhibited  by  magnets 
and  conducting  wires  are  explained  ?  What  is  meant  by  volta-electric  iu- 
ductiou  ? 


314  NATURAL    PHILOSOPHY. 

nected  with  the  battery,  the  outer  coil  will  have  currents  of  elec- 
tricity induced  in  it  as  often  as  the  battery  current  is  broken  or 
the  circuit  completed,  and  only  at  those  times. 

Thus,  let  iy  Fig.  270,  be  a  coil  of  copper  wire,  the  two  ends 

Fig.  270. 


of  which,  A  D,  are  connected  with  a  battery,  and  let  o  be  another 
coil,  placed  over  the  first,  the  two  ends  being  represented  by  the 
two  wires  which  are  held  in  the  hands.  When  the  battery  cur- 
rent is  sent  through  the  inner  coil,  and  when  the  circuit  is  broken, 
there  will  be  induced  in  the  outer  coil  currents  of  electricity, 
which,  if  the  ends  of  the  wire  are  held  in  the  hands,  will  produce 
powerful  shocks.  The  electricity  thus  excited  will  produce  light 
and  heat,  decompose  compounds,  and  produce  all  the  other  effects 
of  the  battery  current.  This  apparatus  is  called  the  Separable 
Helices,  and  is  much  used  for  medicinal  purposes,  as  the  shocks 
can  be  increased  or  diminished  at  pleasure  by  means  of  a  bar  of 
soft  iron,  or  bundles  of  fine  wires,  w,  placed  in  the  inner  coil. 

When  the  wires  are  inserted,  the  shocks  are  wonderfully  in- 
creased through  the  inductive  influence  of  the  magnetism  which 
is  induced  in  them  by  the  battery  current. 

It  is  not  necessary  that  the  second  coil  should  surround  the 
first ;  it  may  only  be  laid  upon  it  or  above  it.  Nor  is  the  effect 
confined  to  the  second  coil ;  but  if  a  third  or  fourth  coil  be  con- 
Desci  ibe  the  separable  helices.  How  may  the  second  coil  be  placed  ? 


SECONDARY  AND  TERTIARY  CURRENTS.        315 

nected  with  the  second,  currents  of  electricity  will  also  "be  induced 
in  them  at  each  interruption  of  the  battery  current. 

Thus,  let  A,  Fig.  271,  be  an  insulated  copper  ribbon  connect- 

Fig.  271. 


ed  with  the  battery,  and  B  a  second  ribbon,  the  two  ends  of 
which  are  connected  with  a  third,  C,  and  a  fourth  coil  of  fine 
wire,  W,  placed  over  this,  with  the  ends  held  in  the  hands. 
When  the  battery  current  is  broken,  currents  will  be  induced  in 
B  and  C,  and  when  they  cease  they  will  induce  currents  in  W, 
which  will  be  manifested  by  giving  a  shock. 

2.  The  currents  in  the  several  coils  move  in  different  directions. 

Thus,  when  the  circuit  is  completed,  a  current  in  the  second 
coil  moves  in  the  opposite  direction,  called  the  initial  current, 
and,  when  it  is  broken,  the  induced  current  flows  in  the  same 
direction,  and  is  called  the  terminal  current.  The  initial  cur- 
rent in  C  will  induce  a  tertiary  current  in  W,  flowing  in  the 
opposite  direction,  and  the  terminal  current  in  C  will  produce  a 
tertiary  current  in  W,  flowing  also  in  an  opposite  direction. 

These  tertiary  currents  are  capable  of  producing  currents  in 
other  helices  of  a  fourth,  fifth,  and  even  the  seventh  order. 

The  direction  of  these  currents,  produced  by  the.  initial  and 
terminal  battery  currents,  are  represented  by  the  signs  +  and 
—  ;  +  when  they  flow  with  the  battery  current,  and  —  when 
they  flow  in  opposite  directions.  Thus,  the 

Initial.  Terminal. 

Battery  or  primary  current -j-  -f- 

Secoridary  current —  -f 

Tertiary  current -f- 

Quaternary  current —  -j- 

What  will  be  the  effect  of  a  series  of  coils  arranged  as  in  Fig.  271  ?  How 
do  the  currents  circulate  in  the  several  bands?  How  are  the  directions  of 
these  currents  indicated  ? 


316 


NATURAL    PHILOSOPHY. 


Fig.  272. 


These  induced  currents,  which  flow  in  opposite  directions,  re- 
act upon  each  other  and  upon  the  battery  current,  and  diminish 
their  effects. 

V.  Magneto-electric  Induction. — Magnets  have  the  power  not 
only  of  inducing  magnetism  in  iron  and  steel,  but  also  currents 
of  electricity  in  conducting  wires. 

Thus,  if  one  pole  of  a  magnet  be  inserted  in  a  coil  or  helix  of 
copper  wire,  the  ends  of  which  are  connected  with  a  galvanome- 
ter, currents  of  electricity  will  be  excited  in  the  coil  when  it  is 
inserted  arid  withdrawn,  as  will  be  indicated  by  the  deflection 
given  to  the  needle. 

But,  for  the  purpose  of  exhibiting  this  effect  in  a  more  satis- 
factory manner,  the  Magneto-electric  Machine  may  be  employed. 

This  consists  of  two  horse-shoe  magnets,  placed  parallel  to  each 
other,  Fig.  272,  with 
an  axis  between  their 
poles,  to  which  is  at- 
tached two  coils  of  cop- 
per wire,  inclosing  bun- 
dles of  iron  wire  in  each, 
constituting  an  arma- 
ture. The  two  ends  of 
the  copper  wire  forming 
the  two  coils  are  sol- 
dered to  a  silver  ferrule 
or  break-piece  on  each 
side  of  the  axis,  against 
which  two  silver  springs 
connected  with  the  two 
cups,  a  b,  press.  The  armature  is  made  to  revolve  by  the  wheel  w. 
As  the  armature  revolves,  and  the  bundles  of  iron  wire  are  brought 
near  the  poles  of  the  magnets,  they  are  rendered  magnetic,  their 
polarities  being  opposite  to  that  of  the  magnets  ;  and  when  the 
wires  pass  between  the  poles  they  lose  their  polarity,  and  acquire 
opposite  polarity  as  they  pass  again  near  the  other  poles  of  the 
magnet.  When  the  polarity  is  changed,  currents  of  electricity 
are  induced  in  the  wire,  and  are  made  to  flow  through  it  to  the 
cups  ;  if  the  revolution  is  rapid,  these  currents  flow  in  a  con- 

What  is  meant  by  magneto-electric  induction  ?  Describe  the  magneto- 
electric  machine.  Describe  the  manner  in  which  currents  of  electricity  are 
induced  by  this  machine. 


AMPERE'S  THEORY. 

tinuous  stream,  and  may  be  made  to  produce  tjesul 
those  produced  by  electricity  from  the  battery. 

But  in  order  to  obtain  powerful  shocks  and 
rents  must  be  interrupted,  as  in  the  battery  current,  and  by  this 
means  secondary  currents  of  much  greater  power  are  induced  in 
the  coil.  This  is  effected  by  means  of  a  steel  spring  connected 
with  one  cup,  as  «,  arid  passing  over  pins  in  a  wheel  connected 
with  the  axis.  When  the  spring  is  pressing  upon  the  pins,  the 
current  flows  in  a  continuous  stream,  and  completes  the  circuit ; 
but  when  it  passes  by  them  the  current  is  broken,  and  at  that 
moment  an  induced  secondary  current  is  given  off  at  the  handles 
connected  with  the  two  cups,  if  they  are  in  contact. 

All  the  effects  of  voltaic  electricity  may  be  produced  by  this 
apparatus.  The  sparks  are  very  bright  at  each  interruption  of 
the  wire,  and  the  shocks  too  powerful  to  be  endured  but  for  a 
moment. 

This  instrument  may  be  employed  for  medicinal  purposes,  for 
decompositions,  for  producing  magnetism  arid  revolutions  of  con- 
ducting wires  and  magnets. 

VI.  Theory  of  Magnetism,  Electro-magnetism,  and  Magneto- 
electricity. — The  most  probable  theory  to  explain  the  facts  of 
magnetism,  electro-magnetism,  and  magneto-electricity  is  that  of 
INI.  Ampere. 

This  theory  rests  upon  the  supposition  that  all  bodies  are  capa- 
ble of  having  circles  of  electricity  excited  in  them,  and  when  the 
circles  in  any  two  coincide  or  are  parallel  to  each  other  they  at- 
tract, and  when  tico  move  in  opposite  directions  they  mutually 
repel  each  other. 

\.  In  the  case  of  steel,  these  currents  are  rendered  permanent 
and  constant  in  one  direction  :  and  in  the  case  of  soft  iron,  they 
are  induced  while  the  battery  current  is  circulating  ;  but  when 
it  ceases,  the  currents  move  in  all  directions  around  the  atoms  of 
which  it  is  composed,  and  neutralize  each  other's  effects. 

By  what  arrangement  are  shocks  and  sparks  produced?  For  what  pur- 
poses may  this  machine  he  employed?  What  theory  best  accounts  for 
magnetism,  &c.  ?  State  the  facts  on  which  the  theory  rests.  Apply  the 
theory  lo  explain  the  action  of  these  currents  on  steel,  iron,  and  the  mag. 
uetic  needle. 


318  NATURAL    PHILOSOPHY. 

2.  The  reason,  then,  that  the  magnetic  needle  turns  to  the 
east  when  the  positive  current  passes  from  north  to  south  above 
it  is,  that  positive  currents  are  constantly  circulating  around  the 
north  pole  of  the  needle  in  a  direction  opposite  to  that  in  which 
the  sun  moves,  and  hence  the  battery  current  opposes  the  current 
of  the  needle,  and  the  north  pole  is  repelled  toward  the  east,  so 
that  both  currents  may  coincide  in  direction ;  and  for  the  same 
reason,  when  the  positive  current  passes  from  north  to  south  be- 
low the  needle,  the  north  pole  is  repelled  toward  the  west,  that 
the  currents  may  again  coincide. 

3.  When  currents  of  electricity  pass  around  soft  iron  or  steel, 
they  induce  currents  in  them  which  move  in  the  same  direction, 
and  then,  if  two  such  pieces  of  steel  are  brought  near  each  other, 
their  north  poles  will  repel,  because  their  currents  flow  in  oppo- 
site directions ;  and  for  the  same  reason  two  south  poles  repel 
each  other.     But  a  north  pole  attracts  a  south  pole  because  the 
currents  coincide  in  direction. 

4.  When  a  magnet  is  brought  near  a  piece  of  iron  or  steel,  it 
converts  it  into  a  magnet,  because  it  induces  currents  of  electricity 
in  it,  which  currents  flow  in  opposite  directions,  and  therefore  a 
north  pole  always  induces  a  south  pole,  and  a  south  pole  a  north. 
This  explains  the  tangential  direction  of  the  magnetic  forces. 

5.  The  tendency  of  the  magnetic  needle  to  stand  north  and 
south  is  readily  explained,  on  the  supposition  that  the  heat  of  the 
sun  and  other  causes  produce  currents  of  electricity,  which  follow 
the  sun  in  his  daily  course  from  east  to  west,  thus  converting  the 
earth  into  a  magnet,  with  the  pole,  which  corresponds  to  the 
north  end  of  the  needle,  toward  the  south.     These  currents  in- 
duce currents  in  the  ores  of  iron,  and  thus  produce  the  loadstone, 
and  give  the  direction  to  the  magnetic  needle ;  for  it  will  be  seen 
that  it  is  only  when  the  needle  stands  north  and  south  that  the 
currents  in  it  and  in  the  earth  coincide  in  direction. 

6.  The  dip  of  the  magnetic  needle  is  due  to  the  fact  that  the 
currents  forming  circles  around  the  earth  are  not  at  right  angles 

What  effect  have  currents  of  electricity  on  soft  iron  and  steel  ?  Explain 
the  reason  lor  the  kind  of  polarity  produced.  Why  does  the  magnetic 
needle  point  north  and  south  1  How  is  the  dip  of  the  magnetic  needle  ex- 
plained 1 


TERRESTRIAL    MAGNETISM. 


319 


Fig.  273. 


to  its  axis,  but  to  a  line  which  dips  below  the  horizon,  called  the 
axis  of  the  magnetic  globe.  The  dip  varies  in  different  parts  of 
the  earth. 

To  illustrate  terrestrial  mag- 
netism, let  Fig.  273  be  a  globe, 
in  the  axis  of  which  a  magnet 
may  be  placed,  and  let  a  coil 
of  wire,  parallel  to  the  equator, 
be  passed  around  it.  If  the 
magnet  is  inserted  in  the  globe, 

t  oU  0"1-J  TT;W,  I  ^Hc^  anc^  a  sma^  magnetic  needle 
k\\  *£&?( — ^nH^\l^]  "  placed  in  various  parts,  it  will 

point  in  the  direction  of  the 
poles,  the  north  pole  of  the  nee- 
dle toward  the  south  pole  of  the 
magnet  in  the  earth.  North 
of  the  equator  the  north  end 
will  dip,  and  the  south  end 
south  of  the  equator.  If  now  the  magnet  be  taken  from  the 
globe,  and  currents  of  electricity  passed  around  under  the  small 
needle,  it  will  have  the  same  directive  tendencies  as  when  the 
magnet  was  inserted,  and  will  stand  toward  the  north  and  south 
poles.  If  it  be  moved  north  or  south  of  the  equator,  it  will  ex- 
hibit all  the  phenomena  of  the  dipping  needle. 

These  experiments  appear  decisive  as  to  the  fact  that  the  mag- 
netism of  the  earth  may  be  due  to  currents  of  electricity  ;  and  in 
the  fact  that  the  heat  of  the  sun  must  produce  currents,  we  have 
all  the  conditions  necessary  to  account  for  the  effect.  This  theory, 
therefore,  will  explain  all  the  phenomena  of  magnetism,  a  sub- 
ject which  is  usually  considered  a  distinct  branch  of  science.* 

*  A  theory  of  magnetism  has  been  proposed  by  William  A.  Norton,  and 
developed  in  the  Journal  of  Science,  vols.  iv.  and  viii.,  in  which  it  is  as- 
sumed that  "  every  particle  of  matter  of  the  earth's  surface,  and  to  a  cer- 
tain depth  below  it,  is  the  center  of  a  magnetic  force,  exerted  tangentially 
to  the  circumference  of  every  vertical  circle  that  may  be  conceived  to  be 
traced  around  it.  The  direction  of  this  force  is  such,  that  to  the  north  of 
the  acting  particle  the  tendency  is  to  urge  the  north  end  downward  and 
the  south  end  upward,  and  to  the  south  of  the  same  particle  it  is  to  urge 
the  north  end  upward  and  the  south  end  downward. 

"  The  intensity  of  the  magnetic  force  of  a  particle  of  the  earth  at  a  g^iven 
distance  is  approximately  proportional  to  its  temperature  or  amount  ot  sen- 
sible heat." 

Illustrate  the  manner  in  which  the  magnetism  of  the  earth  may  be  ac- 
counted for  by  currents  of  electricity. 


320 


NATURAL    PHILOSOPHY. 


VII.  Application  of  Electro-magnetism  to  Useful  Purposes. — 
There  are  many  processes  in  the  arts  which  are  now  conducted 
by  means  of  voltaic  electricity,  especially  the  processes  of  gilding 
and  electrography.  Attempts  have  also  been  made  to  construct 
machines  which  could  be  moved  by  electro-magnetic  power,  and 
although  very  rapid  motions  have  been  attained,  the  requisite 
power  has  not  yet  been  so  applied  as  to  secure  any  very  important 
results.  The  most  useful,  as  well  as  astonishing  application  of 
electricity  which  has  ever  been  made,  is  that  of  making  it  a  mes- 
senger to  convey  intelligence  from  one  place  to  another.  The  in- 
struments to  effect  this  are  called 

Magnetic  Telegraphs. — Of  these  there  are  at  least  three  which 
are  worthy  of  notice — Morses,  House's,  and  Bain's. 

Morses  Magnetic  Telegraph. — This  consists  of  three  parts,  a, 
battery  to  generate  electricity,  conducting  ivires  to  convey  it,  and 
a  register  to  record  the  signs  which  are  used  for  letters. 

The  register  is  represented  in  Fig.  274. 

Tig.  274. 


This  theory,  however,  is  consistent  with  the  idea  that  the  imponderable 
agents  are  the  effects  of  different  vibratory  motions  of  the  particles  of  mat- 
ter, and  of  the  ethereal  undulations  caused  by  them ;  and  hence  the  force 
may  be  electrical.  All  these  views  are  to  be  considered  as  theories,  and 
not  as  settled  facts. 


To  what  uses  has  voltaic  electricity  been  applied? 
telegraph. 


Describe  Morse's 


ELECTRO-MAGNETIC    TELEGRAPH.  321 

It  consists  of  an  electro-magnet,  m  m,  an  armature,  a,  which 
has  a  lever  attached  to  it,  at  the  end  of  which  a  steel  pen,  s,  is 
placed,  to  make  indentations  in  the  paper,  p  p.  The  paper  is 
moved  by  the  clock-work,  c,  over  a  roller,  against  which  the  pen 
is  lifted  when  the  armature  is  attracted  upon  the  magnet.  W  W 
are  wires  which  are  connected  with  the  battery,  at  any  distance 
from  the  register.  Only  one  wire,  however,  is  employed  between 
any  two  stations.  This  is  connected  with  one  pole  of  the  battery 
at  one  end,  and  with  one  cup  of  the  register  at  the  other.  Wires 
are  also  connected  with  the  other  pole  of  the  battery,  and  with 
the  other  cup  of  the  register,  and  passed  into  the  ground. 

To  understand  the  operation  of  this  instrument,  suppose  the 
register  be  placed  in  New  York,  and  a  wire  extending  to  Wash- 
ington connected  with  a  battery.  The  operator  in  Washington 
completes  the  circuit,  and  the  electricity  travels  on  the  wire  to 
New  York,  and  passes  around  the  electro-magnet,  m  m,  by  which 
it  is  rendered  a  magnet,  and  attracts  the  armature,  a,  which  lifts 
the  pen,  s,  against  the  paper,  making  a  dot,  or,  if  the  paper  is  in 
motion,  a  line.  Now  as  often  as  the  circuit  is  broken  the  pen 
fails  from  the  paper,  and  by  completing  and  breaking  the  circuit 
a  series  of  dots  and  dashes  may  be  impressed  upon  it.  As  these 
stand  for  letters,  words  and  sentences  are  readily  communicated 

The  following  is  the  alphabet  used  by  Professor  Morse  : 

2  ----  - 

3  ----- 

4  ------ 

5  --- 

6  ------ 

7  ---- 

8  ----- 

9  ---- 
0  - 


02 


A  

O 

—   _ 

33  

P 

C  

Q 

_ 

D  

R 

_    — 

E  - 

S 



F  

T 



G  

U 



H  

V 



I  -- 

W 



j  

X 

„  — 

K  

Y 

—   — 

L  

Z 

— 

M  

& 

_   .  

N  

322  NATURAL    PHILOSOPHY. 

House's  Telegraph. — This  instrument  is  much  more  compli- 
cated than  the  preceding.  Instead  of  signs,  types  are  used,  and 
each  word  is  printed,  so  as  to  be  read  like  any  other  print. 

Bain's  Telegraph. — This  instrument  does  not  depend  upon 
magnetism,  but  the  electricity  is  made  to  mark  paper  which  is 
chemically  prepared  so  as  to  be  affected  by  it. 

All  the  above  instruments  are  now  in  successful  operation. 
Lines  of  telegraphic  wires  are  rapidly  extending  throughout  the 
United  States  and  Canada.  All  the  most  important  sea-ports 
and  cities  on  the  lakes  are  connected  by  them. 

In  Europe,  also,  telegraphs  are  extensively  employed.  The 
news  received  from  foreign  countries  may  reach  all  parts  of  the 
United  States  at  the  same  moment. 

The  telegraph  is  liable  to  interruptions  from  several  causes. 

1.  The  wires  may  be  broken  by  accident  or  intention. 

2.  Lightning  sometimes  strikes  the  wires,  and  even  electric 
changes,  as  a  thunder-shower  near  the  line,  will  induce  currents 
of  electricity  which  will  cause  the  register  to  work.     A  storm 
may  also  interfere  with  the  regular  communications. 

The  telegraph  has  been  employed  not  only  to  communicate  in- 
telligence, but  also  to  determine  the  longitude  of  different  places, 
and  to  regulate  time-pieces ;  for  as  electricity  passes  instantaneous- 
ly to  any  distance  on  the  earth's  surface,  the  exact  time,  either 
as  indicated  by  observation  upon  the  heavenly  bodies,  or  as  kept 
by  time-pieces,  may  be  accurately  determined,  and  the  difference 
of  longitude  ascertained. 

Dr.  Locke,  of  Cincinnati,  has  lately  invented  a  clock  called 
the  Electro-chronograph,  which,  in  connection  with  a  register,  is 
capable  of  marking  y^th  of  a  second  of  time.  The  clock  breaks 
and  closes  the  circuit  in  such  a  manner  that  the  seconds  are  regis- 
tered in  lines  about  one  inch  in  length,  with  short  breaks  between 
them,  and  the  exact  time  of  any  observation  is  registered  by  touch- 
ing a  key.  This  invention  will  enable  astronomical  observers  to 
note  \vith  great  accuracy  the  time  of  observations,  and  record 

Describe  House's  and  Baiu's  telegraphs.  What  causes  interfere  with  the 
operation  of  the  telegraph?  What  other  uses  of  the  telegraph?  Describe 
the  electro-chronograph  of  Dr.  Locke. 


ANIMAL    ELECTRICITY.  323 

them  at  any  distance  desired,  and  also  to  determine  the  difference 
of  longitude.  It  will  be  of  the  greatest  utility  in  the  survey  of 
coasts  and  harbors,  and  in  all  astronomical  observations,  where 
time  is  so  important  an  element. 

VIII.  Vital  Effects  of  Electricity.— The  effects  of  voltaic  and 
common  electricity  upon  animals  are  similar,  but  the  former  is 
now  more  generally  applied  for  medicinal  purposes.     Electricity 
exerts  a  salutary  effect  in  many  diseases,  and  has  been  supposed 
to  be  intimately  connected  with  the  living  power.     Some  have 
gone  so  far  as  to  assert  that  life  may  be  generated  by  it. 

Its  influence  upon  the  vegetable  kingdom  is  also  most  import- 
ant. The  rocks  and  soils  in  connection  with  the  living  vegetable 
fulfill  the  essential  conditions  of  the  galvanic  battery. 

The  rocks,  too,  are  brought  under  the  influence  of  this  wonder- 
ful power,  and  mineral  veins  are  often  distributed  in  accordance 
with  the  laws  of  voltaic  action. 

IX.  Animal  Electricity.  —  Some  animals  are  capable  of  im- 
parting electric  shocks,  and,  of  course,  of  generating  electricity. 
The  electricity  thus  produced  is  similar  to  that  produced  by 
chemical  action.     This  power  is  possessed  by  several  species  of 
fish.     The  principal  are  the  torpedo  and  the  gyninotus.     The 
torpedo's  power  of  imparting  shocks  was  known  to  Aristotle  and 
Pliny  ;  but  Mr.  Walsh,  in  1773,  made  the  discovery  that  its  shock 
was  precisely  the  same  as  that  of  the  Leyden  jar.     The  electrici- 
ty is  generated  by  certain  organs  just  back  of  the  gills,  on  both 
sides  of  the  body,  about  one  third  of  its  length.     They  resemble 
in  some  respects  a  galvanic  pile,  consisting  of  perpendicular  col- 
umns, amounting  in  some  cases  to  several  hundreds.     These  col- 
umns are  one  fifth  of  an  inch  in  diameter,  and  are  divided  into 
partitions  by  membranes,  making  cells  somewhat  like  those  of  a 
galvanic  battery.     A  new  species  of  this  genus  has  lately  been 
taken   at  Wellfleet,  Massachusetts  (the  Torpedo  occidentalis), 
much  larger  than  the  European  species,  weighing  from  twenty  to 
two  hundred  pounds.     Their  shocks  are  said  to  be  sufficient  to 

Mention  the  vital  effects  of  electricity,  and  its  relations  to  life.  What  is 
animal  electricity?  What  animals  are  capable  of  imparting  shocks  ?  De- 
scribe the  torpedo. 


324  NATURAL    PHILOSOPHY. 

prostrate  a  man.  The  electrical  organs  are  connected  with  a 
very  large  nervous  apparatus,  and  their  power  seems  to  be  de- 
pendent on  the  will  of  the  animal. 

The  Gymnotus  or  Surinam  Eel,  also,  has  the  power  of  im- 
parting powerful  shocks  to  other  animals.  Fish  are  paralyzed, 
and  even  the  wild  horses  which  are  driven  into  certain  lakes  in 
South  America  are  so  paralyzed  by  the  repeated  shocks  from  the 
fish  that  they  are  sometimes  drowned  before  they  can  recover. 
By  these  means  the  eels  become  exhausted,  and  are  easily  captured 
by  the  inhabitants.  This  animal  has  been  subjected  by  Faraday 
to  a  series  of  experiments,  and  the  power  which  it  exercises  has 
been  shown  to  have  a  complete  identity  with  the  electrical  fluid. 
The  animal  is  found  to  be  capable  of  imparting  magnetism  and 
sparks,  producing  heat  and  chemical  decomposition  at  the  time 
of  imparting  the  shock.  Portions  near  the  head  are  found  to  be 
positive,  and  those  near  the  other  extremity  negative.  The  large 
nervous  apparatus  of  this  animal  seems  to  point  out  a  close  con- 
nection between  electricity  and  nervous  power.  It  has  been  sug- 
gested that  nervous  power  may  become  electrical  under  a  cer- 
tain state  of  the  system. 

The  Silurus  Electricus,  found  in  regions  of  Africa,  possesses 
also  a  similar  electrical  power. 

Nature  of  Electricity. — In  exhibiting  the  phenomena  of  elec- 
tricity it  seemed  necessary  to  conceive  of  this  agent  as  a  fluid, 
but  the  more  probable  view  is,  as  has  already  been  stated,  that 
electricity,  light,  and  heat  are  dependent  upon  certain  modifica- 
tions of  the  same  substance  called  the  ether  ;  that  its  production 
depends  upon  certain  motions  of  this  ether,  and  its  transmissions 
upon  its  undulations,  connected,  it  may  be,  with  certain  states  or 
vibrations  of  ponderable  matter. 

For  a  more  extended  treatise  on  magnetism  and  electro-mag- 
netism, the  student  is  referred  to  Davis' s  Manual  of  Magnetism, 
from  which  several  of  the  diagrams  in  this  work  were  taken. 

Describe  the  Surinam  eel.     What  is  the  nature  of  electricity  ? 


OPTICS.  325 

CHAPTER  IX. 

LIGHT,  OR    OPTICS. 

Optics  is  that  branch  of  Natural  Philosophy  which  treats  of 
the  nature  and  phenomena  of  light. 

This  science  properly  embraces  whatever  relates  to  the  origin 
and  sources  of  light ;  to  the  laws  which  govern  its  transmission ; 
to  its  relations  to  ponderable  matter  ;  to  color  arid  vision ;  and  to 
the  theories  by  which  its  nature  is  illustrated  and  its  phenomena 
are  explained. 

Light,  in  its  nature,  as  has  already  been  indicated,  is  analo- 
gous to  sound.  It  is  produced  by  undulations  of  an  ether  which 
is  supposed  to  pervade  all  space,  and  vision  is  the  effect  of  these 
undulations  upon  the  retina  of  the  eye. 

The  proof  of  this  view  of  the  nature  of  light  will  be  adduced 
after  considering  its  origin,  and  describing  some  of  its  obvious 
phenomena,  such  as  radiation,  reflection,  refraction,  decomposi- 
tion, absorption,  &c. 

It  is  unnecessary  to  say  that  this  constitutes  a  most  interesting 
branch  of  natural  science,  whether  we  contemplate  it  in  regard 
to  the  exquisite  coloring  of  flowers,  the  opaline  plumage  of  birds, 
the  many-tinted  leaves  of  the  autumnal  forest,  the  gorgeous  hues 
imparted  by  the  rising  or  setting  sun  to  his  attendant  clouds,  or 
to  its  boundless  utility  to  man  in  the  supply  of  his  wants,  and  the 
preservation  of  his  existence. 

"  Man,"  says  Arnott,  "wherever  placed  in  light,  receives  by 
the  eye  from  every  object  around,  nay,  from  every  point  in  every 
object  and  at  every  moment  of  time,  a  messenger  of  light  to  tell 
him  what  is  there,  and  in  what  condition.  Were  he  omnipresent, 
or  had  he  the  power  of  flitting  from  place  to  place  with  the  speed 
of  the  wind,  he  could  scarcely  be  more  promptly  informed.  Then, 
in  many  cases  where  distance  intervenes  not,  light  can  impart  at 

Define  optics.  What  does  the  science  embrace?  What  is  said  of  the 
nature  of  light? 


326  NATURAL    PHILOSOPHY. 

once  knowledge,  which,  by  any  other  conceivable  means,  could 
come  only  tediously,  or  not  at  all.  For  example,  when  the  illu- 
minated countenance  is  revealing  the  secret  working  of  the  heart, 
the  tongue  would  in  vain  try  to  speak,  even  in  long  phrases,  what 
one  smile  of  friendship  or  affection  can  in  an  instant  convey. 
Had  there  been  no  light,  man  never  could  have  suspected  the  ex- 
istence of  the  miniature  worlds  of  life  and  activity  which,  even 
in  a  drop  of  water,  the  microscope  discovers  to  him  ;  nor  would 
he  have  formed  any  idea  of  the  admirable  structure  of  many 
minute  objects.  It  is  light,  also,  which,  pouring  upon  the  eye 
through  the  optic  tube,  brings  intelligence  of  events  passing  in 
the  remotest  regions  of  space." 

SECTION  L— ORIGIN  OF  LIGHT,  AND  THE  LAWS  WHICH  GOVERN  ITS 

TRANSMISSION. 

I.  Light  originates  in  ponderable  matter,  and  is  developed 
by  heat,  chemical  and  voltaic  action,  and  by  the  presence  of  lu- 
minous bodies,  as  the  sun  and  stars. 

II.  Bodies  may  be  divided  into  self-luminous  and  non-lumi- 
nous, opaque,  transparent,  and  translucent.      That  ivhich  trans- 
mits light  is  called  a  medium. 

III.  In  the  same  medium,  rays  of  light  move  in  straight 
lines.      This  is  proved  by  the  position  of  the  images  of  bodies 
and  by  the  phenomena  of  shadows. 

IV.  The  intensity  of  light  radiating  from  a  luminous  point 
is  inversely  as  the  square  of  the  distance.      The  intensity  is  de- 
termined, \.  By  the  comparison  of  shadows  ;  2.  By  equally  il- 
luminated surfaces  ;  and,  3.  By  the  power  of  causing  a  shadow 
to  disappear. 

V.  The  velocity  of  light  is  about  195,000  miles  per  second. 
This  has  been  ascertained  in  two  ways :  by  observations  upon 
the  eclipses  of  the  satellites  of  Jupiter,  and  by  the  aberration  of 
the  stars. 

I.  Origin  of  Light. — The  existence  of  ponderable  matter  is 
as  necessary  to  the  production  of  light  as  to  that  of  sound.  A 
vacuum  may  transmit  it,  but  can  not  generate  it.  Matter,  as 

How  does  light  originate  ? 


SOURCES    OF    LIGHT.  327 

has  been  seen,  consists  of  minute  atoms,  and  these  individually 
are  so  closely  connected  with  producing  the  phenomenon  of  light, 
that  they  may  be  considered  as  luminous  points  from  which  it 
emanates. 

All  matter,  when  heated  to  a  certain  temperature,  gives  out 
light.  In  solids,  this  temperature  is  977°  Fahrenheit  (Draper), 
but  in  gases  it  is  much  higher.  The  light  emitted  is  at  first  of 
a  dull  red  color ;  but  it  increases  in  brightness,  in  a  rapid  ratio, 
as  the  temperature  is  raised,  a  body  yielding,  at  2600°,  a  light 
of  a  dazzling  whiteness,  nearly  forty  times  as  intense  as  at  1000°. 

Artificial  light  is  usually  produced  by  chemical  action,  as  in 
ordinary  combustion,  and  the  light  proceeding  from  voltaic  elec- 
tricity. In  this  case,  it  is  always  connected  with  heat. 

There  are  some  mineral,  and  certain  decayed  vegetable  and 
animal  substances,  which  shine  in  the  dark,  and  are  said  to  phos- 
phoresce— a  phenomenon  which  has  been  ascribed  to  slow  com- 
bustion. Certain  animals,  also,  as  the  glow-worm,  emit  light 
from  their  bodies,  which  may  be  seen  in  the  dark. 

But  the  great  source  of  our  light  is  the  sun,  which  sends  it 
forth  in  all  directions  through  the  regions  of  space.  The  stars 
shine  with  their  own  light,  and  many  of  them,  from  their  superior 
magnitude,  pour  forth  floods  of  this  dazzling  fluid,  much  more  in- 
tense than  that  which  we  receive  from  our  sun,  but  their  immense 
distance  renders  it  faint  and  powerless  to  us.  The  moon  and 
planets  generate  no  light,  but  only  reflect  that  which  they  receive 
from  the  sun. 

II.  Bodies  are  divided  into  self-luminous,  or  such  as  shine  by 
their  own  light,  as  the  sun,  stars,  and  terrestrial  lights,  and  non- 
luminous,  or  those  which  only  reflect,  absorb,  or  transmit  the 
light  of  luminous  bodies. 

Those  bodies  which  do  not  permit  light  to  pass  through  them 
are  called  opaque ;  those  which  offer  little  or  no  resistance  to  its 
passage  are  termed  transparent ;  and  those  which  but  partially 
transmit  it  are  said  to  be  translucent.  Opaque  bodies,  when  made 
into  very  thin  leaves,  are  translucent,  as  gold  and  silver  leaf. 

What  are  the  sources  of  terrestrial  light?  What  other  sources  of  light? 
What  division  is  made  of  bodies  in  their  relation  to  light? 


328  NATURAL    PHILOSOPHY. 

That  which  transmits  light  is  called  a  medium.  Gases,  liq- 
uids, and  transparent  solids  impede  its  passage  more  or  less,  and 
are  therefore  imperfect  media.  A  vacuum  is  a  perfect  or  free 
medium. 

A  ray  of  light  is  a  line  of  luminous  particles  proceeding  from 
a  luminous  point ;  a  beam  of  light  is  a  number  of  parallel  rays  ; 
and  a  pencil  of  light  is  a  collection  of  rays,  radiating  from  a  lu 
ruinous  point. 

III.  Laws  of  the  transmission  of  light. 

1 .  In  the  same  medium,  rays  of  light  proceeding  from  a 
luminous  point  move  in  straight  lines,  and  with  uniform  ve- 
locity. 

(1.)  That  light  moves  in  straight  lines,  is  shown  by  the  phe- 
nomena of  images.  If  a  ray  of  light  be  admitted  through  a 
small  aperture  into  a  dark  room,  it  falls  upon  the  wall  at  a  point 
directly  opposite  the  aperture  and  its  source  ;  and  if  the  air  be 
agitated,  the  line  of  the  ray  may  be  distinctly  seen  by  means  of 
the  floating  moats  which  are  illuminated  by  the  ray. 

(2.)  When  a  pencil  of  rays  falls  upon  an  opaque  body,  the 
form  of  the  shadow  shows  that  the  lines  described  are  straight 
lines. 

Thus,  suppose  a  pencil  of 
rays  proceed  from  the  point  . 
A,  Fig.  275,  and  fall  upon 
the  opaque  ball,  B,  the  lines 
A  C  and  A  D  will  be  straight 
lines,  as  is  shown  by  the  limits  of  the  shadow  beyond  B. 

The  shadow  in  this  case  will  be  conical,  and  will  increase  in 
size  the  further  it  proceeds  beyond  B.  If  the  luminous  body 
have  any  considerable  magnitude,  there  will  be  formed  a  half 
shadow  on  each  side  of  the  perfect  shadow. 

That  part  of  the  central  shadow  which  receives  no  light  is 
called  the  umbra,  while  that  which  receives  light  from  some 
parts  of  the  luminous  body  and  not  from  others,  is  termed  the 


What  is  a  medium?  when  is  it  free?  Define  a  ray,  a  beam,  and  a  pen 
oil  of  light.  What  is  the  law  of  the  transmission  of  light?  What  is  the 
umbra,  and  what  the  penumbra  ? 


PHENOMENA  OF  ShADOWS.  329 

Thus,  let.  A,  Fig  276,  be 
d  luminous  body,  as  the  sun, 
and  ii  Ei  an  opaciue  body. 
-^__  The  space  H  B  E  receiving 

~  "^^GSi)  no  light,  will  be  the  umbra. 
But  the  light  from  d  will  shine  upon  the  space  H  B  C,  while 
that  from  f  will  be  wholly  obstructed  ;  and  the  same  is  true  of 
the  space  H  E  D,  which  receives  light  from  /,  but  riot  from  d  ; 
hence  these  spaces  will  be  partially  illuminated. 

It  will  be  noticed  that  the  form  of  the  penumbra  is  that  of  an 
inverted  cone,  and  that  it  increases  in  diameter  the  farther  it 
proceeds  from  the  opaque  body.  But  the  umbra,  or  dark  shadow, 
will  have  a  form  depending  upon  the  relative  magnitude  of  tbe 
luminous  and  the  opaque  body.  If  the  luminous  body  is  less  than 
the  opaque,  it  will  increase  in  size  as  it  proceeds,  as  in  Fig.  275. 
-  277.  If  the  two  bodies  are  equal, 

it  will  be  in  the  form  of  a 
cylinder,  as  in  Fig.  277. 

If  the  luminous  body  is 
larger  than  the  opaque,  the 
umbra  will  converge  to  a  point,  as  in  Fig.  276.  In  all  cases, 
the  depth  of  the  shadow  is  greatest  and  most  clearly  defined  im- 
mediately behind  the  opaque  body,  for  both  the  umbra  and  the 
penumbra  fade  away  at  a  great  distance  from  it.  It  is  for  this 
reason  that  the  shadow  of  the  point  of  a  steeple  is  not  accurately 
defined,  while  that  of  a  hair,  held  near  a  white  screen,  is  perfectly 
marked. 

Whatever  the  form  of  the  shadow,  the  lines  of  light  which 
limit  it  are  always  straight  lines.     That  light  moves  with  uni- 
form velocity,  is  proved  by  observations  upon  Jupiter's  satellites. 
2.  When  a  luminous  point  or  surface  sends  rays  of  light  into 
a  dark  chamber  upon  a  screen  or  reflecting  surface,  through 
a  small  orifice,  there  is  formed  an  exact  image  of  the  luminous 
body,  whatever  the  form  of  the  aperture  through  -which  it  passes. 
This  fact  is  easily  shown  by  allowing  rays  of  light  to  pass  into 
a  darkened  room,  through  a  small  aperture  in  the  shutter. 

How  are  the  forms  of  shadows  determined  ?     What  is  the  form  of  the 
images  formed  by  luminous  objects  ? 


330  NATURAL    PHILOSOPHY. 

Thus,  if  the  direct  rays  of  the  sun  **- 278- 

be  admitted  into  a  room  through  a 
square  aperture,  as  o,  Fig.  278,  a 
pencil  of  rays  from  each  point  of  the 
sun's  surface  will  enter  through  the 
aperture,  and  form  square  images 
upon  the  screen,  as  at  c.  As  the  sun  is  round,  there  will  be  a 
series  of  these  quadrangular  images,  produced  by  rays  from  the 
circular  edge  of  the  sun,  disposed  in  a  circle  upon  the  screen, 
while  the  light  from  the  central  parts  of  the  sun  will  fill  up  the 
interior  space  with  similar  images,  and  the  result  will  be  a  circu- 
lar illuminated  figure,  which  will  be  an  exact  image  of  the  sun. 

Hence,  if  the  light  which  passes  through  the  aperture  be  re- 
flected from  an  opaque  body,  we  shall  have  an  inverted  image  of 
the  object  upon  the  screen.  It  is  on  this  principle  that  the  hu- 
man eye  and  camera  obscura,  which  will  be  described  in  a  future 
section,  are  constructed. 

IV.  Intensity  of  Light. —  The  intensity  of  light,  radiating 
from  a  luminous  point,  varies  inversely  as  the  square  of  the  dis- 
tance. This  may  be  proved  mathematically  and  by  experiment. 

Thus,  if  a  luminous  point  be  placed  in  the  center  of  a  hollow 
sphere,  it  will  send  rays  to  all  parts  of  the  inner  surface.  If  the 
same  quantity  of  light  be  placed  in  a  sphere  whose  radius  is  two, 
three,  or  four  times  as  great,  it  will  be  distributed  over  the  entire 
surface.  Now  the  surfaces  of  spheres  are  as  the  squares  of  their 
radii ;  and  hence,  if  the  radius  of  one  sphere  be  twice  or  three 
times  greater  than  that  of  another,  its  surface  will  be  four  or  nine 
times  as  great,  and  the  same  quantity  of  light  being  spread  over 
this  whole  surface,  its  intensity  will  be  only  one  fourth  or  one 
ninth  as  great.* 

This  law  may  be  shown  experimentally,  by  allowing  a  ray  of 
light  to  pass  from  a  point,  A,  Fig.  279,  upon  square  pieces  of 
board,  placed  at  the  distance  of  1,  2,  3,  and  4  feet  from  it,  as  B, 
C,  D,  E.  The  first  board,  B,  will  obstruct  all  the  light  from 
C,  or  the  same  quantity  of  light  which  fell  upon  B  would  be 

*  This  law,  as  applied  to  the  intensity  of  gra\7itation,  was  demonstrated 
geometrically  on  page  37,  Fig.  15.  The  same  demonstration  applies  to  the 
intensity  of  light,  or  to  any  influence  radiating  from  a  point. 

What  is  the  law  of  the  intensity  of  light  at  different  distances  1 


rilOTOMETHY.  331 

spread  over  C,  D,  or  E.     These  surfaces,  C,  D,  and  E5  will  be 

Fig.  279. 


B  ODE 

found  to  contain  four,  nine,  and  sixteen  times  the  surface  of  B ;  and 
hence  the  light  must  be  only  {th,  |th,  and  y^th  as  intense  as  at  B. 

This  proposition  is  strictly  true,  however,  only  when  the  light 
proceeds  from  a  small  surface  or  point,  moves  through  a  vacuum, 
and  falls  perpendicularly  upon  the  surface. 

If  the  surface  is  oblique,  it  is  evident  that  the  same  quantity 
of  rays  will  be  spread  over  a  larger  surface,  as  is  exhibited  in  the 
falling  of  the  oblique  rays  of  the  sun  upon  the  northern  and  south- 
ern portions  of  the  earth's  surface.  In  passing  through  the  at- 
mosphere, or  any  transparent  medium,  some  of  the  rays  of  light 
are  impeded  ;  therefore  the  intensity  actually  diminishes  rather 
faster  than  the  squares  of  the  distances  increase. 

Photometry. — In  order  to  measure  the  comparative  intensities 
of  different  lights  at  the  same  distance,  and  of  the  same  light  at 
different  distances,  several  methods  have  been  employed. 

1.  It  may  be  done  by  the  comparison  of  shadows.  This 
method  depends  upon  the  fact  that  the  deeper  the  shadows  cast 
by  opaque  bodies,  the  more  intense  must  be  the  light. 

Fig.  280.  ^  Thus,  let  A,  Fig.  280,  be  a  screen  of  white 
paper,  d  a  rod,  and  C  E  two  lights,  placed  at 
equal  distances  from  the  rod,  so  as  to  cast  two 


IjXirT Pt  shadows  from  it  upon  the  screen.  By  observ- 
ing these  shadows,  it  is  easy  to  tell  which  is 
the  darker.  Then,  by  removing  the  light 
which  casts  the  deeper  shade,  until  the  two  shadows  are  equally 
dark,  and  measuring  the  distances  of  the  lights  from  d,  their  illu- 
minating powers  will  be  ascertained,  for  they  will  be  as  the  squares 

What  circumstances  modify  the  intensity  of  light?    How  are  the  intensi- 
ties of  different  lights  determined  ? 


332 


NATURAL    PHILOSOPHY. 


of  their  distances.  If  the  two  shadows  are  equally  dark,  and 
the  light  C  is  twice  the  distance  of  JE  from  the  rod,  then  the 
light  of  C  is  four  times  as  intense  as  that  of  E.  If  C  is  three 
or  four  times  the  distance  of  E,  its  light  will  be  nine  or  sixteen 
times  as  bright. 

2.  A  second  method  is  by  the  equal  illumitiation  of  surfaces. 
The  instrument  by  which  this  is  effected  is  called 

Ritchie's  Photometer. 
— It  consists  of  a  box,  a  b, 
Fig.  281,  in  the  center 
of  which  is  a  wedge,  cov- 
ered with  white  paper,  f 
e  g,  and  a  conical  tube  in 
the  top,  through  which 
the  eye  can  look  down 
on  the  screen,  and  which 
may  be  raised  or  lowered 
by  the  stand  c. 

To  determine  the  intensities  of  two  lights,  the  one,  m,  is  placed 
so  as  to  illuminate  the  surface  ef,  and  the  other,  n,  the  surface 
e  g.  The  eye,  at  d,  can  observe  both  surfaces  at  the  same  time, 
and  the  lights  are  then  placed  at  such  distances  that  both  sur- 
faces appear  equally  illuminated.  The  intensities  of  light  they 
give  out  will  be  as  the  squares  of  their  distances  from  the  screen. 
Thus,  if  m  be  twice  the  distance  of  n,  when  both  sides  of  the 
screen  are  equally  illuminated,  it  gives  out  a  light  four  times  as 
intense. 

3.  There  is  still  a  third  method,  which  is  considered  more  val- 
uable than  either  of  the  preceding.     It  depends  upon  the  principle 
that  a  shadow  will  be  imperceptible  in  the  presence  of  a  light 
sixty-four  times  as  intense  as  that  by  which  it  is  cast.     For  ex- 
ample, take  two  lights  whose  intensities  \ve  wish  to  compare, 
and  ascertain  the  relative  distances  at  which  they  will  cause  the 
shadow  cast  by  a  third  light  to  disappear,  and  their  intensities  will 
be  as  the  squares  of  these  distances.     The  eye  can  judge  of  the 
disappearance  of  the  shadows  more  accurately  than  of  the  depth 
of  the  shadows,  or  of  the  intensity  of  the  illumination.     For  this 
reason  this  method  is  the  most  accurate  of  an v  hitherto  invented. 


Mention  the  several  methods  of  determining  the  intensities  of  different 
lights.     Which  is  the  best  ? 


VELOCITY    OF    LIGHT.  333 

V.  Velocity  of  Light. — The  velocity  of  light  has  been  determ- 
ined by  two  methods,  entirely  independent  of  each  other. 

1.  Its  velocity  was  first  determined  by  Roemer,  in  1676,  from 
observations  upon  Jupiter's  satellites.     It  was  observed  that  when 
the  earth  was  nearest  Jupiter,  one  of  the  satellites  of  this  planet 
appeared  to  enter  its  shadow,  or  to  emerge  from  it,  about  16 
minutes  sooner  than  when  the  earth  was  on  the  opposite  side  of 
its  orbit,  or  at  its  greatest  distance  in  its  annual  revolution.    The 
distance  between  the  two  points  of  observation  was  the  diameter 
of  the  earth's  orbit,  or  about  190,000,000  miles,  and  therefore  it 
was  inferred  that  it  took  light  a  little  more  than  16  minutes  to 
traverse  this  space. 

To  illustrate,  let  S,  Fig.  282,  be  the  sun,  E  the  earth,  and  T  the 
Fig.  282.  first  satellite  of  Ju- 

piter.  This  satel- 
lite passes  through 
the  shadow  of  its 
primary,  from  T  to 
T',  in  42  hours  28 
minutes,  and  the 
earth  moves  dur- 
ing the  same  time 
from  E  to  E',  a  dis- 
tance  of  2,880,000 
miles.  But  the  satellite  actually  emerges  from  the  shadow  fif- 
teen seconds  later  than  it  v/ould  if  the  earth  had  remained  at  E  ; 
and  hence  the  light  is  fifteen  seconds  in  passing  from  E  to  E', 
or  2,880, 000  miles,  which  would  make  its  velocity  192,000  miles 
per  second. 

That  light  moves  uniformly  at  this  rate,  is  shown  by  making 
the  observations  when  the  earth  is  in  different  parts  of  its  orbit, 
either  farther  or  nearer  to  Jupiter  than  is  shown  in  the  diagram. 
In  all  cases  the  rate  per  second  will  be  the  same. 

2.  Dr.  Bradley,  in  1725,  confirmed  this  result  by  the  aberra- 
tion of  the  stars,  by  which  is  meant  an  apparent  change  in  regard 
to  their  actual  place  in  the  heavens.     This  is  produced  by  the 
combined  motion  of  light  and  of  the  earth  in  its  orbit. 

By  whom  was  the  velocity  of  light  first  determined  ?  by  what  means? 
illustrate  by  diagram.  What  is  the  velocity  of  light  as  determined  by  this 
method  ? 


331  NATURAL    PHILOSOPHY. 

It  may  be  illustrated  in  the  following  manner  :  Fig.  283. 
Let  S  A  and  S'  B,  Fig.  283,  be  two  rays  of  light 
coming  from  a  star  or  the  sun  to  the  earth  moving 
in  its  orbit  in  the  direction  A  B.  If  now  a  telescope 
be  held  in  the  direction  A  S,  the  ray  S  A,  in  con- 
sequence of  the  motion  of  the  earth  from  A  toward 
B,  will  impinge  upon  the  side  of  the  tube  before  it 
reaches  the  bottom.  But  if  the  telescope  be  placed 
in  the  direction  A  E,  so  that  A  B  shall  be  to  A 
S  as  the  velocity  of  the  earth  to  the  velocity  of 

light,  the  ray  will  reach  the  bottom  of  the  tube, 

passing  through  S'  E  A  ;  and  hence  the  star  will 
appear  at  S'when  it  is  actually  at  S.  The  angle  S  A  S'  is 
called  the  angle  of  aberration.  This  amounts  to  20£  seconds  for 
each  star.  By  this  method  the  velocity  of  light  was  found  to  be 
195,000  miles  per  second,  a  result  so  nearly  coinciding  with  that 
derived  from  Jupiter's  satellites,  as  to  leave  no  doubt  that  the 
true  velocity  of  light  is  very  accurately  determined. 

SECTION  II.— REFLECTION  OF  LIGHT,  OR  CATOPTRICS. 

1.  When  a  ray  of  light  is  reflected,  1.  The  angles  of  inci- 
dence and  of  reflection  are  equal ;   2.  When  rays  of  light  fall 
upon  plane  mirrors,  the  reflected  rays  have  the  same  inclination 
as  the  incident  rays  have  ;  and,  3.  The  images  formed  by  plane 
mirrors  correspond  with  the  objects,  being  at  the  same  distance 
from  the  mirror,  and  like  situated  in  every  respect. 

4.  When  two  mirrors  are  placed  at  an  angle,  two  o*  more 
images  of  the  object  are  formed. 

II.  Rays  of  light  falling  on  curved  surfaces  observe  the  same 
laiv  ;  hence,  1.  Parallel  rays  falling  upon  a  concave  mirror  are 
reflected  to  a  point  called  the  focus  of  parallel  rays,  ivhich  is 
half  way  between  the  center  of  curvature  and  surface  of  the 
mirror.  Concave  mirrors  give  rise  to  images,  whose  position 
and  magnitude  will  depend  upon  the  position  of  the  object. 

2.  Rays  of  light  falling  upon  a  convex  mirror  are  rendered 
diverging ;  and  hence  the  images  of  such  mirrors  are  less  than 
the  object  behind  the  mirror,  and  nearer  to  it  than  the  object. 

RAYS  of  light  proceeding  from  a  luminous  body  in  the  same 

What  other  method  has  been  employed  to  ascertain  the  velocity  of  ligb*  7 
Illustrate  what  is  meant  by  the  aberration  of  the  stars. 


REFLECTION    OF    LIGHT.  335 

medium,  move,  as  we  have  seen,  in  right  lines.  But  when  they 
fall  upon  the  surface  of  opaque  bodies,  they  are  either  thrown 
back — that  is,  reflected — or  taken  up  by  the  body,  in  which  case 
they  are  said  to  be  absorbed.  When  they  fall  upon  transparent 
solid  or  liquid  surfaces,  or  pass  from  one  medium  to  another,  they 
are  turned  from  a  straight  line,  and  are  said  to  be  refracted.  Let 
us  first  attend  to  the 

Reflection  of  Light. —  When  a  ray  of  light  falls  upon  a 
smooth  opaque  surface,  it  is  throivn  back,  and  is  said  to  be  re- 


For  instance,  if  a  ray  of  light  pass  into  a  dark  room,  and  fall 
upon  a  polished  metallic  surface,  there  is  seen  a  bright  spot  upon 
it ;  and  if  all  the  rays  are  reflected,  the  surface  is  not  seen,  but 
only  the  light.  The  surface  of  a  perfectly  polished  substance  is 
not  visible.  It  is  owing  to  the  irregularity  of  reflected  rays, 
arising  from  the  irregularity  of  the  surfaces  from  which  they 
come,  that  any  object  becomes  visible  to  the  eye.  Surfaces  which 
reflect  most  of  the  rays  of  light  are  called  mirrors. 

1.  Laws  of  Reflection. —  1.  A  ray  of  light  falling  upon  a 
smooth  surface  is  reflected  in  such  a  manner,  that  the  angle  which 
the  line  described  by  the  incident  ray  makes  at  the  point  of  inci- 
dence with  a  perpendicular  to  tliat  point  is  always  equal  to  the 
angle  made  by  the  line  described  by  the  reflected  ray  and  this 
same  perpendicular ;  or,  in  other  words,  the  angle  of  incidence 
is  equal  to  the  angle  of  reflection,  and  is  in  the  same  plane. 

Fig.  284.  Let  c,  Fig.  284,  be  a  plane  surface,  d  c  the  line 

/a  described  by  the  ray  falling  upon  the  surface  at  the 
point  c,  arid  c  b  a  perpendicular  to  that  point.    Then 
c  a  will  be  the  path  of  the  reflected  ray,  and  the 
\    /  angle  d  c  b,  called  the  angle  of  incidence,  will  be 

\  / ^    equal  to  the   angle  b  c  a,   called  the   angle  of 

c  '  reflection.  Light,  in  this  respect,  follows  the 
same  law  as  solid  or  liquid  bodies,  when  they  fall  upon  plane 
surfaces. 

Light  may  be  reflected  from  plane  or  convex  mirrors. 

2.  W  hen  rays  of  light  fall  upon  plane  mirrors,  the  reflected 

What  is  meant  by  reflection,  refraction,  and  absorption  of  light?  Illus- 
trate the  reflection  of  light.  What  is  the  law  of  reflection  ? 


336 


NATURAL    PHILOSOPHY. 


Fig.  285. 


Fig.  286. 


rays  have  the  same  inclination  to  each  other  as  the  incident  rays 
have.     This  fact  is  a  direct  result  of  the  preceding  law. 

The  incident  rays  may  be  parallel,  converging,  or  diverging. 

(1.)  If  the  parallel  rays,  a  c,  b 
d,  Fig.  285,  fall  upon  the  mirror, 
A  B,  the  reflected  rays,  cft  d  e, 
will  also  be  parallel.*  If  the  in- 
cident rays  are  in  the  same  plane, 
the  reflected  rays  will  also  be. 

(2.)  If  the  rays,  a  c,  b  d,  Fig.  286,  fall  converging  upon  the 
mirror,  A  B,  the  reflected  rays 
will  converge,  as  c  e,  d  e,  and 
meet  in  the  point  e. 

(3.)  But  if  the  rays  e  d,  e  c 
fall  diverging  upon  the  mirror, 
A  B,  then  the  reflected  rays  will 
diverge  in  the  direction  d  b  and 
c  a  ;  that  is,  will  have  the  same 
inclination  as  the  incident  rays. 

3.  Images  formed  by  Plane  Mirrors. — In  this  case,  the  reflect- 
ed rays  give  rise  to  an  image 
of  the  luminous  point  or  object, 
which  will  appear  as  far  behind 
the  mirror  as  the  object  is  be- 
fore it ;  for  the  two  reflected 
rays,  c  e,  df,  Fig.  287,  if  con- 
tinued back,  will  meet  at  a', 
arid  by  letting  fall  a  perpen- 
dicular  from  a  to  the  mirror, 
and  continuing  it  to  the  same 
distance  behind  the  mirror,  it 
will  meet  the  point  a'.f 

On  this  principle  it  is  possible  to  construct  the  image  of  any 
object  as  formed  by  a  mirror. 

*  For  the  angle  a  c  f=b  d  c  and/c  B  =.e  d  B  being  opposite  exterior 
and  interior  angles,  therefore  c/is  parallel  to  e  d. 

t  The  two  right-angled  triangles,  a  c  h  and  a'  c  h  are  equal,  because 
they  have  a  common  side,  h  c,  and  the  angle  h  c  a  =  h  c  a1  and  c  h  a  = 
c  k  a';  consequently,  a  h  is  equal  to  h  a'. 

Mention  the  several  laws  of  reflection  from  plane  mirrors.  Describe  the 
nvmner  in  which  images  are  formed  by  plane  mirrors.  By  what  rule  may 
the  image  be  constructed  1 


„    2g7 


IMAGES    OF    PLANE    MIRRORS. 


337 


711 


Thus,  let  A  B,  Fig.  288,  be  an 
object  placed  before  a  plane  mirror, 
m'  m.  The  rays,  A  g,  A/,  will  be 
reflected  in  the  direction  f  E,  g  o. 
These  two  lines  produced  will  meet 
at  a,  and  the  perpendicular,  A  a, 
will  meet  in  the  same  point.  The 
same  will  be  true  of  the  rays  from 
B ;  they  will  be  reflected  to  E  and  o 
as  if  they  came  from  b  ;  and  hence 
there  will  be  an  image  of  these  two 
points  at  the  same  distance  behind 
the  mirror  as  the  two  points  actual- 
ly are  before,  it.  The  same  effect 
will  be  produced  by  the  rays  pro- 
ceeding from  every  part  of  the  object  between  A  and  B  :  and 
hence  the  image  a  b  will  be  at  the  same  distance  behind  the  mir- 
ror that  the  object  A  B  is  before  it,  and  will  be  similarly  situated 
in  every  respect. 

If,  therefore,  a  plane  mirror  be  placed  at  an  angle  of  45°  to 
the  horizon,  an  erect  object  placed  before  it  will  appear  horizon- 
tal, and  a  horizontal  object  erect,  because  the  image  will  have 
the  same  inclination  to  the  mirror  as  the  object ;  and  as  each  is 
45Q,  taken  together,  they  will  amount  to  90°. 

When  the  object  is  twice  the  length  of  the  mirror,  and  placed 
parallel  to  it,  its  image  will  be  distinctly  seen,  for  the  angle  of  re- 
flection is  equal  to  the  angle  of  incidence,  and  these,  taken  to- 
gether, are  double  the  angle  of  incidence.  The  surface,  therefore, 
which  reflects  the  rays  from  the  object  will  be  but  half  as  long  or 
as  broad  as  the  object ;  hence  a  person  may  see  his  whole  length 
in  a  mirror  which  is  but  half  of  his  height. 

4.  The  distinctness  or  brightness  of  the  image  increases  as  the 
angle  of  incidence  increases.  For  example,  if  the  light  of  a 
lamp  fall  nearly  perpendicularly  upon  ground  glass,  polished 
wood,  or  varnished  paper,  we  can  not  distinguish  any  flame ; 
but  if  the  rays  fall  obliquely,  the  image  will  be  distinctly  seen  ; 
that  is,  the  intensity  of  the  reflected  rays  is  least  at  perpendicular 
incidence,  and  increases  with  the  angle  of  incidence.  The  in- 

What  relation  does  the  image  bear  to  the  object?  Upon  what  does  the 
brightness  of  the  image  depend  ? 

P 


338 


NATURAL    PHILOSOPHY. 


"Fig.  289. 


tensity  of  the  reflected  rays  is  modified,  also,  by  the  medium  in 
which  they  move,  and  the  nature  of  the  surface  against  which 
they  impinge. 

5.  Angles  of  Reflection. —  When  two  mirrors  are  placed  to- 
gether at  certain  angles,  two  or  more  images  are  formed. 

Thus,  let  A  B,  C  B,  Fig. 
289,  be  two  plane  mirrors, 
placed  at  right  angles  to  each 
other,  and  a  a  luminous  point. 
The  rays  af  and  a  g  falling 
upon  the  two  mirrors,  will  be 
reflected  to  I,  and  an  eye  at 
this  point  will  see  two  images 
of  a  at  E  and  b.  But  the 
ray  a  K  will  be  reflected  to 
c,  and  then,  by  a  second  re- 
flection, to  I,  so  that  the  eye 
will  perceive  a  third  image  at 
d  ;  that  is,  the  image  of  a  at  K  will  send  rays  to  c,  and  form  by 
reflection  a  second  image  at  d. 

By  making  the  angle  less  than  90°,  the  number  of  images  will 
be  increased,  the  image  formed  by  one  reflection  constituting  an 
object  or  radiant  point  for  a  second  image,  and  this  for  a  third. 
If  the  inclination  of  the  mirrors  be  60°,  45°,  and  30°,  there  will 
be  six,  eight,  and  ten  images  disposed  in  a  circular  manner. 

When  the  mirrors  are  parallel  the  number  of  images  will  be- 
come indefinite,  and  their  situation  will  be  in  a  direct  line.  In 
consequence  of  the  diminution  of  light  by  repeated  reflections,  the 
images  are  less  and  less  brilliant,  until  the  light  becomes  too  feeble 
for  them  to  be  perceived. 

This  principle  is  illustrated  in  what  is  called 

The  Endless  Gallery,  which  consists  of  a  box,  having  two 
plane  mirrors  placed  parallel  to  each  other  in  the  opposite  sides. 
When  any  object,  as  a  candle,  is  placed  in  the  box,  there  is  pre- 
sented an  endless  succession  of  images.  A  person  standing  be- 
tween two  mirrors  placed  upon  the  opposite  walls  of  a  room  may 
see  images  of  himself  reflected  in  the  same  manner. 

How  may  several  images  of  an  object  be  formed  ?     What  will  be  the 
ber  of  images  when  two  plane  mirrors  are  placed  parallel  to  each  other  ? 


CURVED    MIRRORS. 


339 


The  Kaleidoscope  is  also  constructed  on  the  same  principle. 

Two  glass  mirrors  are  inserted  in  a  tube  at  an  angle  of  30°  or 
60°,  and  pieces  of  colored  glass  are  so  placed  as  to  exhibit  an 
endless  variety  of  images  as  the  tube  is  turned. 

IT.  Reflection  from  Curved  Mirrors. — Curved  surfaces  may 
be  concave  or  convex.  A  hollow  sphere,  or  the  section  of  one, 
whose  inner  surface  is  polished,  constitutes  a  concave  mirror,  and 
the  same  polished  externally  a  convex  mirror.  The  same  law 
of  reflection  applies  to  curved  mirrors  as  to  plane,  the  angle  of 
incidence  being  always  equal  to  the  angle  of  reflection.  But,  in 
consequence  of  the  curvature,  the  reflected  rays  take  the  same 
direction  that  they  would  if  they  fell  upon  a  plane  which  is  tan- 
gent to  the  curve  at  the  point  of  incidence. 

For  illustration,  let  A  r  s 
B,  Fig.  290,  be  a  curved  mir- 
ror, C  the  center  of  a  sphere 
of  which  it  forms  a  part,  A 
B  its  diameter,  in  tn'  its  axis, 
passing  through  the  middle  of 
A  B,  and  the  lines  C  A  and 
C  B  its  aperture.  Rays  of 
light  proceeding  from  C  will 
fall  perpendicularly  upon  the 
concave  surface,  and  will  be 
reflected  to  C  ;  or  if  they  fall 
upon  the  convex  surface,  as 
a  s,  they  will  be  thrown  back 
in  the  same  path.  But  rays  of  light  proceeding  from  F  to  r  will 
be  reflected  in  the  direction  r  o,  on  the  other  side  of  the  perpen- 
dicular, C  r,  just  as  they  would  be  if  they  fell  upon  the  plane, 
k  fcf,  which  is  a  tangent  at  the  point  r.  If  a  ray  fall  upon  the 
convex  surface,  as  d  s,  it  will  be  reflected  in  the  direction  s  b,  and, 
on  the  other  side  of  the  line,  a  s,  perpendicular  to  the  tangent  at  the 
point  s.  The  path  of  the  reflected  ray  is  determined  by  making 
the  angle  b  s  a  equal  to  d  s  a,  or  C  r  o  equal  to  C  r  F.  By  ob- 
serving this  law,  we  may  determine  with  geometrical  precision 
the  path  of  any  reflected  ray. 

Let  us  apply  this  law  to  concave,  and  then  to  convex  surfaces. 


Describe  the  kaleidoscope.    Define  a  curved  mirror.    Illustrate  the  man- 
ner in  which  rays  of  light  are  reflected  from  curved  surfaces. 


340  NATURAL    PHILOSOPHY. 

1.  Concave  Mirrors.  —  Let 
a  c,  Fig,  291,  be  a  section  of 
a  concave  mirror,  C  its  center, 
and  the  line  A  B  its  axis ;  we 
may  then  determine  the  path 
of  the  reflected  rays  when  the 
radiant  or  luminous  point  is 
placed  at  different  distances 
from  the  mirror. 

Suppose  the  radiant  be  so  far  TV 

removed  that  the  ray  h  a  shall  be  parallel  to  the  axis  A  B  ;  it 
will  be  reflected  to  the  point  F,  and  this  point  is  determined  by 
making  the  angle  C  a  F  equal  to  C  a  h.  Now  the  angles  C  a 
F  and  F  C  a  are  equal,  and  F  a  will  be  therefore  equal  to  F  C  ; 
and  if  the  ray  h  a  is  very  near  the  axis,  F  a  will  be  very  nearly 
equal  to  F  B ;  or  the  ray  h  a  will  be  reflected  to  a  point  half 
way  between  the  center  of  the  curve  and  the  surface  of  the  mir- 
ror. This  point  is  called  the  principal  focus,  or  the  focus  of 
parallel  rays;  for  all  the  rays  parallel  with  the  axis  and  near 
to  it  will  be  collected  very  nearly  in  this  point.  Hence  parallel 
rays  of  light  falling  upon  a  concave  mirror,  parallel  to  the 
axis,  are  reflected  to  a  point  called  the  principal  focus,  which  is 
half  way  between  the  center  of  concavity  and  the  surface  of  the 
mirror, 

Suppose  the  radiant  to  be  placed  at  A,  then  the  ray  A  a  will 
be  reflected  to  e,  a  point  between  the  center  of  concavity  and  the 
principal  focus.  As  A  approaches  C,  the  angle  of  incidence,  A  a 
C,  will  diminish,  and,  consequently,  the  angle  of  reflection,  C  a  e, 
will  diminish,  and  e  will  approach  c,  so  that  when  the  radiant  is 
in  the  center  of  concavity,  the  angle  of  incidence  being  nothing, 
the  reflected  ray  will  return  to  C  ;  and  if  the  radiant  be  removed 
toward  F,  the  reflected  rays  will  pass  on  the  other  side  of  the 
perpendicular,  C  a,  and  will  cut  the  axis  beyond  C,  along  the 
line  B  A.  When  the  radiant  arrives  at  F,  the  reflected  rays 
will  become  parallel.  If  the  radiant  be  moved  from  F  toward 

Illustrate  the  mode  of  determining  the  paths  of  rays  reflected  from  a 
concave  mirror  when  the  radiant  occupies  different  positions.  How  is  the 
focus  of  parallel  rays  determined  ?  How  far  is  the  focus  from  the  surface 
of  the  mirror? 


IMAGES    OF    CONCAVE    MIRRORS.  341 

B,  11  is  evident  that  the  reflected  rays  will  diverge,  as  a  d,  more 
and  more,  until  the  radiant  reaches  the  surface.     Hence, 

(1.)  Diverging  rays  radiating  from  a  point  of  the  axis  farther 
from  the  mirror  than  the  center  of  concavity,  and  falling  upon  a 
concave  mirror,  are  reflected  to  the  axis  at  a  point  between  the 
center  and  the  principal  focus. 

(2.)  Diverging  rays  radiating  from  the  center  of  concavity  are 
reflected  hack  again  to  the  same  point. 

(3.)  Diverging  rays  radiating  from  any  point  between  the  cen- 
ter of  concavity  and  the  principal  focus  are  reflected  so  as  to  cut 
the  axis  at  points  beyond  this  center. 

(4.)  Rays  diverging  from  the  focus  are  reflected  in  parallel 
lines. 

(5.)  .Diverging  rays  proceeding  from  any  point  between  the 

principal  focus  and  the  surface  of  the  mirror  are  reflected  diverging. 

(6.)  If  converging  rays  fall  upon  the  surface,  it  is  evident  that 

they  will  be  converged  to  a  point  between  the  principal  focus  and 

the  surface  of  the  mirror. 

(7.)  In  all  these  cases  the  radiant  is  supposed  to  be  situated 
in  the  axis,  but  the  path  of  the  reflected  ray  may  be  easily  de- 
termined if  the  radiant  is  situated  on  either  side  of  the  axis. 

If  the  radiant  is  at  d,  Fig.  291,  the  ray  d  a  will  be  reflected 
on  the  other  side  of  the  axis,  at  the  same  distance  from  it  as  d. 

2.  Images  formed  by  Concave  Mirrors. — Having  pointed  out 
the  method  of  determining  the  paths  of  reflected  rays  of  light, 
Fig  292.  when  the  position  of  the  radi- 

ant is  known,  it  is  easy  to  de- 
termine the  position  and  rela- 
tive magnitudes  of  the  images 
which  are  formed  by  concave 
mirrors. 

Let  M  M',  Fig.  292,  be  a 
concave  mirror,  F  the  princi- 
pal  focus,  C  the  center -of  con- 
cavity, and  D  r  its  axis. 

Mention  the  several  conditions  under  which  rays  of  light  may  fall  upon 
a  concave  mirror,  and  the  paths  of  the  reflected  rays.  Illustrate  the  mode 
in  which  images  are  formed  by  concave  mirrors. 


342 


NATURAL    PHILOSOPHY. 


Fig.  293. 


(1.)  If  the  object  be  placed  in  the  center  of  concavity,  C,  the 
image  will  coincide  with  it.  This  is  seen  when  a  mirror  is  held 
so  that  the  eye  is  in  its  center,  C. 

(2.)  If  the  object  be  between  the  center  and  principal  focus,  as 
A  B,  the  image  will  appear  beyond  the  center,  inverted  and  lar- 
ger, as  a  b  ;  and,  consequently, 

(3.)  If  the  object  be  beyond  the  center,  the  image  will  be  be- 
tween the  center  and  principal 
focus  ;  if  a  b  is  the  object,  A  B 
wifl  be  the  image.  When  the 
object  is  at  an  infinite  distance 
the  image  will  be  in  the  prin- 
cipal focus. 

(4.)  If  the  object  is  between 
the  principal  focus  and  the  mir- 
ror, as  A  B,  Fig.  293,  the  im- 
age will  be  behind  the  mirror, 
erect  and  larger,  as  a  b. 

As  concave  mirrors  generally  form  their  images  in  front  of  the 
mirror,  they  were  once  employed  to  produce  surprising  appear- 
ances, the  mirror  being  concealed  in  the  wall  to  reflect  an  image 
of  any  object,  so  that  it  might  appear  in  the  air  or  upon  a  cloud 
produced  for  the  purpose. 

Concave  reflectors  have  been  employed  for  telescopes  for  light- 
houses, either  to  concentrate  the  rays  of  light  or  throw  them  in 
a  particular  direction. 

3.  Convex  Mirrors.  —  In 
convex  mirrors  the  path  of  the 
reflected  ray  is  determined  by 
the  same  law  as  that  of  con- 
cave mirrors.  But  as  the  rays 
fall  upon  the  external  surface 
of  a  sphere,  such  mirrors  have 
only  an  imaginary  focus. 

Let  s  s',  Fig.  294,  be  a 
convex  mirror,  and  c  the  cen- 
ter, c  v  its  axis,  and/ its  focus. 
All  these  points  are  on  the 


Fig.  294. 


What  uses  have  been  made  of  concave  mirrors  ?    How  is  the  path  of  the 
reflected  ray  determined  in  convex  mirrors  ? 


IMAGES    OP    CONVEX    MIRRORS.  343 

side  opposite  to  that  on  which  the  light  falls,  but  still  it  is  equally 
easy  to  determine  the  direction  of  the  reflected  rays. 

(1.)  If  the  rays  converge  toward  the  center  of  concavity,  p  s, 
p'  s,  they  will  return  by  the  same  paths,  because  they  strike  the 
plane,  tangent  to  the  parts  at  s  s',  at  right  angles. 

(2.)  If  the  rays  converge  toward  the  principal  focus,  as  t  s,  V  s', 
they  will  be  reflected  in  the  direction  s  r,  s'  rf,  in  lines  parallel 
tq  the  axis ;  and  hence  parallel  rays  will  be  reflected  in  lines 
which,  if  continued,  would  meet  in  the  principal  focus ;  hence  they 
will  diverge  after  reflection. 

Rays  proceeding  from  any  point  of  the  axis,  and  falling  upon 
the  surface,  will  all  be  divergent  after  reflection. 

(3.)  Images  of  Convex  Mirrors. —  The  images  of  convex  mir- 
rors are  situated  behind  the  mirror,  are  less  than  the  object,  and 
symmetrical  with  it,  whatever  be  the  position  of  the  object. 

Fig.  295.  Thus,  let  M'  M,  Fig.  295, 

be  a  convex  mirror,  and  A  B  an 
object  placed  before  it.  The 
rays  from  A  and  B  will  be  re- 
fleeted  to  E  as  if  they  came 
from  a  b;  hence  an  eye  placed 
at  E  will  perceive  a  diminish- 
ed image  of  the  object,  and  the 
ME  Bame  will  be  true  wherever  the 

object  is  placed,  because  the  reflected  rays  will  diverge  after  re- 
flection in  all  positions  of  an.  object,  and  will  therefore  appear  to 
come  from  points  behind  the  mirror,  and  nearer  to  its  surface  than 
the  object ;  hence  the  images  must  be  smaller. 

3.  Spherical  Aberration. — When  parallel  rays  of  light  fall 
upon  a  concave  mirror,  those  rays  near  the  axis  are  not  converged 
to  the  same  point  as  those  further  from  it ;  and  hence  pencils  of 
rays  from  all  parts  of  an  object  will  not  be  collected  at  exactly 
the  same  points ;  hence  the  image  will  be  indistinct.  By  the 
crossing  of  the  reflected  rays,  there  is  produced  a  curve  more 
brilliant  than  other  parts,  called  the  caustic  curve. 

To  avoid  the  aberration  produced  by  concave  mirrors,  they  are 
sometimes  ground  in  a  parabolic  form,  and  then  all  the  rays  which 
fall  upon  their  surfaces  are  reflected  accurately  to  a  focal  point. 

Point  out  the  paths  of  the  reflected  rays.  What  kind  of  images  are  form- 
ed by  convex  mirrors  ?  Illustrate  what  is  meant  by  spherical  aberration. 
How  may  it  be  remedied  ?  What  are  caustic  curves  ? 


344  NATURAL    PHILOSOPHY. 


SECTION  III.— DIOPTRICS,  OR  REFRACTION  OF  LIGHT. 

I.  When  light  passes  obliquely  from  one  medium  to  another 
of  different  density,  it  is  refracted. 

1 .  If  a  ray  of  light  pass  from  a  rarer  into  a  denser  medium, 
it  is  bent  toward  a  perpendicular  to  the  refracting  surface. 

2.  If  from  a  denser  to  a  rarer  medium,  it  is  bent  from  a  per- 
pendicular to  the  refracting  surface.    The  ratio  between  the  sines 
of  the  angle  of  incidence  and  of  refraction  is  called  the  index  of 
refraction. 

3.  This  ratio  may  be  such  that  a  ray  will  not  pass  from  a 
denser  to  a  rarer  medium,  and  will  give  rise  to  what  is  called 
total  reflection. 

4.  If  a  ray  pass  through  a  medium  bounded  by  plane  and  par- 
allel surfaces,  the  incident  and  emergent  rays  will  be  parallel. 

II.  When  a  beam  of  light  passes  through  a  triangular  prism 
near  the  refracting  angle,  1.  It  will  be  turned  toward  the  back 
of  the  prism;  2.  When  rays  from  a  single  object  fall  upon  sev- 
eral surfaces  inclined  to  each  other,  several  images  of  the  object 
may  be  seen. 

III.  1.  When  parallel  rays  of  light  fall  upon  convex  lenses, 
they  are  converged  to  a  point  called  the  principal  focus,  the  dis- 
tance of  ivhichfrom  the  lens  will  depend  ttpon  its  form  and  com- 
position. 

2.  The  action  of  concave  lenses  upon  rays  of  light  is  just  the 
opposite  to  that  of  convex  lenses. 

3.  Convex  lenses  form  inverted  images  of  objects. 

4.  Concave  lenses  do  not  form  convergent  images  of  objects^ 
but,  when  looked  through,  we  may  see  erect  diminished  images. 

5.  Owing  to  the  laws  of  refraction,  all  the  rays  which  fall 
upon  a  convex  lens  are  not  converged  to  the  same  point ;  and 
hence  we  have  what  is  called  the  spherical  aberration  of  lenses. 

6.  Heat  always  accompanies  solar  light ;  and  hence  convex 
lenses  are  burning  glasses. 

IV.  When  a  beam  of  light  is  passed  through  a  prism  it  is 
separated  into  seven  differently-colored  rays,  which  are  arranged 
in  an  invariable  order,  and  called  the  solar  spectrum. 


LAWS    OF    REFRACTION.  345 

V.  Certain  appearances  in  nature  are  explained  by  the  re' 
flection  and  refraction  of  light,  such  as  the  rainbow,  twilight, 
haloes,  and  mirage. 

WE  have  seen  that  light  moves  in  the  same  medium  in  straight 
lines,  but  when  it  passes  from  one  medium  to  another  of  different 
density,  as  from  air  into  water,  it  is,  with  few  exceptions,  bent 
from  a  direct  course,  and  this  deviation  or  change  of  direction  is 
called 

Refraction.  —  1.  To  illustrate,  let  «, 
Fig.  296,  be  a  point  from  which  a  ray 
of  light  passes  in  the  direction  a  S,  and 
falls  obliquely  upon  the  surface  of  water, 
A  B.  At  the  point  S  the  ray  will  be 
bent  out  of  a  straight  line ;  that  is,  in- 
stead of  proceeding  to/,  it  will  be  refract 
ed  to  e,  or  toivard  a  perpendicular,  p  p', 
to  the  refracting  surface.  The  same  law 
will  always  prevail  wherever  a  ray  passes 
from  a  rarer  to  a  denser  medium,  excepting  when  the  ray  falls 
perpendicularly  upon  the  surface  of  the  medium,  in  which  case 
no  deviation  will  take  place. 

2.  If  a  ray  of  light  proceed  from  e,  and  pass  out  of  the  water 
into  the  air,  it  will  be  bent  at  the  surface,  S,  and,  instead  of  pro- 
ceeding to  b,  will  be  refracted  toward  a,  or  from  a  perpendicular 
to  the  refracting  surface. 

1.  Laws  of  Refraction. — It  may  be  stated,  then,  as  a  general 
law,  1.  That  a  ray  of  light,  in  passing  from  a  rarer  to  a  denser 
medium,  is  bent  toward  a  perpendicular  to  the  refracting  sur- 
face;  and, 

2.  That  a  ray  of 'light  passing  from  a  denser  to  a  rarer  me 
dium,is  bent  from  a  perpendicular  to  the  refracting  surface. 

There  is  but  one  exception  to  these  laws,  and  that  is  when  a 
ray  falls  perpendicularly  upon  the  surface  ;  but  the  ray  may  fall 
so  obliquely  that,  in  passing  into  a  rarer  medium,  the  refraction 
is  so  great  as  to  prevent  it  from  entering,  in  which  case  it  is  re- 
flected at  the  surface. 

Define  refraction  of  light.  Illustrate  by  diagram.  What  is  the  law  of 
refraction  ? 


346 


NATURAL    PHILOSOPHY. 


The  line  described  by  the  ray  before  it  meets  the  surface  is  called 
the  incident  ray,  and  that  which  it  describes  after  refraction  the 
refracted  ray.  The  angle  A  S  P  is  called  the  angle  of  incidence, 
e  s  p'  the  angle  of  refraction,  and  e  sfihe  angle  of  deviation. 

As  objects  are  seen  in  the  direction  in  which  light  from  them 
meets  the  eye,  it  is  easy  to  prove,  both  by  experiment  and  from 
observation,  the  truth  of  the  laws  of  refraction  which  have  been 
given.  Fig.  297. 

If  we  take  a  vessel,  A  B  C  D,  Fig. 
297,  and  lay  a  half  dollar  in  the  bot- 
tom at  O,  and  place  the  eye  at  E,  so 
that  a  ray  of  light  proceeding  direct- 
ly from  the  coin  would  have  to  pass 
through  the  sides  of  the  vessel,  O  G  Ei 
E,  just  below  the  top,  it  is  evident 
that  the  coin  would  not  be  visible. 
But  if  the  vessel  be  partly  filled  with  water,  the  light  from  the 
coin  will  be  bent  from  a  perpendicular,  P  Q,  at  the  point  L,  so 
as  to  pass  over  the  edge  of  the  vessel  into  the  eye  at  E,  and  ren- 
der the  coin  visible.  It  will  appear  to  be  raised  up,  as  at  K,  be 
cause  E  K  is  the  apparent  direction  of  the  light. 

This  is  the  reason  that  water  in  a  river  or  pond,  whose  bottom 
may  be  seen,  appears  to  be  more  shallow  than  it  actually  is,  and 
that  any  object,  as  an  oar,  partly  immersed  in  water*,  appears 
bent  at  the  surface. 

2.  Indices  of  Refraction. — In  order  to  exhibit  the  relation 
between  the  angles  of  incidence  and  of  refraction, 

Let  A  P  B,  Fig.  298,  be  a  globe 
half  full  of  water,  and  C  a  point  in  its 
center,  upon  which  a  ray  of  light  may 
fall  from  I,  and  be  refracted  to  R,  I 
C  P  will  be  the  angle  of  incidence, 
and  II  C  P  the  angle  of  refraction. 
The  lines  I  m,  H  R,  let  fall  from  I 
and  R  upon  P  P,  a  perpendicular  to 
the  refracting  surface,  are  called  the 
sines  of  the  angles  of  incidence  and 
of  refraction. 

Which  is  the  angle  of  incidence,  and  which  the  angle  of  refraction  ?  What 
effect  has  refraction  upon  the  position  of  objects?  What  is  meaut  by  indi- 
ces of  refraction  ? 


Fig.  298. 


INDICES    OF    REFRACTION.  347 

Now  it  is  found  by  experiment  that,  with  the  same  medium, 
the  sines  of  the  angles  of  incidence  and  of  refraction  bear  to  each 
other  a  constant  ratio;  that  is,  if  the  line  I  m  is  double  that  of 
H  R,  then  I'  m'  will  be  double  H'  K/,  or  whatever  the  angle  at 
which  the  ray  meets  the  surface,  the  line  representing  the  angle 
of  incidence  will  always  be  double  that  which  represents  the  an- 
gle of  refraction. 

Thus,  in  the  case  of  rays  of  light  passing  from  air  into  water, 
the  ratio  of  the  sines  of  incidence  #nd  of  refraction  is  as  1'366 
to  1  ;  that  is,  if  H  R  be  1, 1  m  wiU  be  1-366 ;  or  if  H'  R'  be  1, 
I"  m'  will  be  T366,  and  the  same  ratio  would  exist  at  whatever 
angle  the  ray  might  pass  from  air  into  water.  But  this  ratio 
varies  for  different  substances.  From  air  into  crown-glass  these 
lines  are  in  the  ratio  of  T53  to  1,  and  into  diamond  as  2'487  to 
1.  These  ratios,  determined  for  each  substance  by  experiment, 
are  arranged  in  tables,  and  called  Indices  of  Refraction. 

The  following  table  contains  the  indices  of  refraction  for  sev- 
eral substances.  The  sine  of  the  angle  of  refraction  is  called  1, 
and  that  of  incidence  is  represented  as  follows  : 

Indices  of  Refraction.  Indices  of  Refraction. 


Chromate  of  lead 2-974 

Diamond 2-487 

Sulphur 2-148 

Rock  crystal 1-548 


Crown  glass 1-530 

Flint  glass 1-584 

Water 1-366 

Ice 1-309 


If  we  would  estimate  rightly  the  refractive  powers  of  different 
substances,  we  must  regard  their  specific  gravities  or  densities ; 
for  if  a  less  dense  body  is  as  refractive  as  one  more  dense,  its  ab- 
solute refractive  power  must  be  much  greater.  On  this  principle 
hydrogen  gas,  the  lightest  of  any  known  substance,  has  an  index 
of  refraction  over  3.  Combustible  bodies  generally  have  the  high- 
est indices  of  refraction. 

3.  Total  Reflection. — The  constant  ratio  between  the  sines  of 
the  angles  of  incidence  and  of  refraction  renders  it  impossible  for 
a  ray  of  light  to  pass  out  of  a  denser  into  a  rarer  medium,  when 
the  angle  of  refraction  causes  the  ray  to  make  an  angle  with  the 
surface  equal  to  or  exceeding  90°. 

Are  the  indices  of  refraction  the  same  for  all  bodies  ?  Under  what  con- 
ditions does  total  reflection  take  place  ? 


348 


NATURAL    PHILOSOPHY. 


For  example,  if  the  ray  /  e,  Fig. 
299,  passing  out  of  a  dense  medium, 
a  b  c,  meet  the  surface,  b  e,  so  that 
the  angle  of  refraction  would  cause 
the  ray  to  make  with  the  surface  an 
angle  of  90°  or  more,  it  is  evident 
that  it  can  not  pass  out  of  the  me- 
dium, but  will  be  reflected  at  its  sur- 
face, and  will  be  seen  as  at  d.  This 
is  called  total  refection,  because  all  the  rays  so  situated  must  be 
reflected  ;  and  this  is  the  only  case  of  a  perfect  mirror.  In  all 
other  cases  of  reflection  some  of  the  rays  are  either  absorbed, 
transmitted,  or  scattered.  Such  a  surface,  therefore,  exhibits  the 
highest  possible  brilliancy. 

The  angle  of  total  reflection  will  depend  upon  the  indices  of 
refraction.  From  water  into  air,  it  is  48°  28' ;  from  glass,  it  is 
about  41°  55'  ;  from  diamond,  23°  35'. 

4.  When  light  passes  through  any  medium  which  is  bounded 
by  surfaces  that  are  plane  and  parallel  to  each  other,  into  the 
same  medium  in  which  it  tvas  moving  before  refraction,  the 
emergent  and  incident  rays  are  always  parallel. 

Thus,  if  the  rays  r  s,  b  c,  Fig.  300, 
pass  from  air  through  the  solid  rectangu- 
lar piece  of  glass,  A  B,  the  emergent  rays, 
d  e,  g  f,  will  be  parallel  to  the  incident 
rays,  r  s,  b  c.  The  reason  of  this  is,  that 
the  emergent  rays  at  d  g  will  be  bent  just 
as  far  from  as  the  incident  rays  at  s  c 
were  toward  a  perpendicular  to  the  re- 
fracting surface. 

Hence,  if  the  incident  rays  are  parallel,  the  emergent  rays  will 
also  be  parallel ;  if  convergent,  they  will  be  convergent ;  and  if 
divergent,  they  will  be  divergent.  Therefore,  objects  seen  through 
such  media,  as  through  a  pane  of  glass,  will  have  the  same  mag- 
nitude, and  will  but  slightly  vary  in  position  from  their  position 
when  seen  through  air  alone. 

If,  however,  diverging  rays  pass  out  of  a  denser  into  a  rarer 

What  is  the  law  of  incident  and  emergent  rays  when  light  is  transmitted 
through  bodies  whose  surfaces  are  plane  and  parallel  ?  What  influence  is 
exerted  on  convergent  and  divergent  rays  ? 


REFRACTION    OP    LIGHT    BY    PRISMS.  349 

medium,  a?  they  will  be  refracted  from  a  perpendicular  to  the 
surface,  their  divergency  will  be  increased.  If  they  pass  out  of 
a  rarer  into  a  denser  medium,  they  will  diverge  less  than  before, 
because  they  are  refracted  toward  a  perpendicular  to  the  refract- 
ing surface. 

II.  Refraction  of  Light  by  Prisms.— An  optical  prism  is  a 
Fig.  301.  transparent  medium,  bounded  by  two  surfaces  which 
incline  to  each  other  ;  the  line  of  their  intersection  is 
called  the  edge,  and  the  angle  which  they  make  the 
refracting  angle  of  the  prism. 

A  prism  consists  generally  of  a  triangular  piece  of 
glass,  a,  Fig.  301,  mounted  upon  a  stand,  b,  and  a 
joint,  c,  to  enable  us  to  place  it  in  any  position. 

1 .  When  a  ray  of  light  passes  through  a  prism  near  the  re- 
fracting angle,  it  is  turned  toward  the  back  of  the  prism,  while 
the  object  is  removed  toward  the  refracting  angle. 

Let  ABC,  Fig.  302,  be  a  tri- 
angular prism,  C  the  refracting  an- 
gle, and  a  b  a  ray  of  light  incident 
upon  the  surface,  A  C.  The  ray 
will  first  be  refracted  to/,  and  as 
it  emerges  on  the  side  B  C,  it  will 
again  be  refracted  toward  d,  and 
an  eye  at  this  point  would  there- 
fore see  the  object  removed  down- 
ward to  a1 ;  and  if  the  refracting 
C  angle  were  turned  upward,  all  ob- 

jects would  appear  to  be  raised  up  from  their  actual  position ; 
that  is,  the  objects  are  always  removed  in  the  direction  of  the  re- 
fracting angle  of  the  prism.  The  intersection  of  the  lines  a  b, 
f  d,  at  e,  ibrming  the  angle  a  e  a',  is  called  the  angle  of  devia- 
tion. The  larger  the  refracting  angle,  the  greater  the  deviation. 

The  refracting  power  of  the  substance,  and  the  direction  in 
which  the  rays  fall  upon  the  surface,  influence  the  degree  of  de- 
viation. It  is  found  by  experiment  and  by  calculation,  that  the 
angle  of  least  deviation  is  equal  to  the  index  of  refraction,  mi- 
nus one,  multiplied  by  the  refracting  angle  of  the  prism. 

Define  a  prism.  Illustrate  the  law  of  refraction  in  prisms.  What  is  the 
angle  of  deviation,  and  to  what  is  it  equal  1 


350 


NATURAL    PHILOSOPHY. 


2.  When  light  falls  upon  several  surfaces,  so  that  tttfe  rays,  after 
refraction,  shall  approach  each  other,  several  images  are  produced. 
Glasses  constructed  for  this  purpose  are  called 

Multiplying    Glasses.  —  Fig.  303. 

Thus,  let  a  ray  of  light  from 
a,  Fig.  303,  fall  upon  A  F, 
and  emerge  from  the  five 
surfaces  A  B,  B  C,  C  D,  D 
E,  E  F,  so  inclined  to  each 
other,  that  the  rays,  after  re- 
fraction, shall  meet  at  I,  an 
eye  situated  at  this  point 
will  see  five  images  of  a,  and 
the  number  of  images  may 
be  greatly  increased  by  multiplying  the  number  of  faces. 

III.  Refraction  by  Lenses. — A  lens  consists  of  a  transparent 
substance  whose  bounding  surface  is 
curved.    There  are  six  kinds  of  lenses, 
as  seen  in  Fig,  304. 

The  plano-convex  lens,  A,  is  bound- 
ed by  one  plane  and  one  convex  sur- 
face. 

The  plano-concave,  B,  is  bounded 
by  one  plane  and  one  concave  surface. 

The  double  or  bi-convex  lens,  C,  is 
bounded  by  two  convex  surfaces  ;  and  F 

The  double  concave,  D,  by  two  concave  surfaces. 

The  concavo-convex  lenses,  E,  F,  have  one  concave  and  one 
convex  surface.  E  is  termed  a  meniscus  lens.  They  differ  from 
each  other  hi  the  fact  that  the  concavity  of  the  surface  of  F  is 
less  than  the  convexity,  but  in  E  it  is  equal  or  greater. 

A,  C,  and  F  are  thicker  at  their  centers  than  at  the  edges, 
and  are  convergent  lenses  ;  while  B,  D,  and  E  are  thinner  at, 
their  centers  than  at  the  edges,  and  are  divergent  lenses. 

Lenses  are  generally  made  of  glass,  though  sometimes  of  rock 
crystal  and  other  precious  stones,  as  the  diamond.  They  are 


How  may  objects  be  multiplied  by  refraction  1     Describe  the  several 
kinds  of  lenses.     Of  what  are  lenses  made  ? 


REFRACTION    BY    LENSES. 


351 


ground  to  spherical  surfaces,  though  there  are  elliptical,  parabol 
ic,  cylindrical,  and  other  forms  given  to  them. 

In  the  double  convex  lens,  a  b,  Fig. 
305,  c  and/  are  the  centers  of  the  curva- 
ture, or  geometrical  centers  ;  d  is  the  op- 
tical center,  a  b  the  aperture,  c  f  the 
axis,  and  m  n  the  secondary  axis.  All 
the  rays  which  pass  through  the  optical 
center,  as  m  n,  f  c,  are  called  principal 
rays.  They  are  the  central  rays  of  each 
pencil  of  light,  which  proceeds  from  any 
luminous  object. 
The  refraction  of  light  by  lenses  may  be  understood  by  means 
of  a  prism  whose  refracting  angle  is  very  small.  The  deviation 
in  such  a  prism  may  be  regarded  as  very  nearly  in  proportion  to 
the  refracting  angle  ;  that  is,  one  prism  whose  refracting  angle  is 
twice  as  great  as  that  of  another,  will  produce  twice  the  devi- 
ation. Each  prism  must  have  the  same  index  of  refraction. 

We  have  seen  that  light  is  bent  toward  the 
back  of  the  prism.     If,  therefore,  we  put  the 
backs  of  two  prisms  of  very  small  refracting 
angles  together,  as  a  b  c  and  c  b  d,  Fig.  306, 
and  let  the  parallel  rays  of  light  from  f  and 
g  pass  through  them,  they  will  be  bent  to  F, 
where  they  will  meet ;  or,  if  rays  proceed  from 
F,  they  will  be  rendered  parallel. 
Now  we  may  regard  a  double  convex  lens  as  composed  of  an 
indefinite  number  of  plane  surfaces,  situated  so  as  to  form  a 
curve,  upon  which  parallel  rays  may  fall,  and  be  converged  to  a 
focal  point. 

In  the  same  way,  by  uniting  the  re- 
fracting angles  of  two  prisms,  o  r  s,  s  t  v, 
as  in  Fig.  307,  and  letting  the  parallel 
rays  from  e  and /pass  through  them,  the 
71  rays  will  diverge  as  they  emerge  from  the 
second  surface  to  g  and  h.  A  double  con- 
cave lens  is  precisely  similar  in  its  action 
upon  light. 

Illustrate  by  diagram  the  axis,  geometrical  and  optical  centers,  and  aper- 
ture of  lenses.  What  are  principal  rays  ?  How  may  the  refraction  of  light 
by  lenses  be  illustrated  ? 


ff 


352  NATURAL    PHILOSOPHY. 

These  two  forms  of  lenses  are  exactly  opposite  in  their  effects 
upon  light. 

1.  Convex  Lenses. — The  action  of  all  convex  lenses  is  similar. 
The  difference  in  their  effects  depends  chiefly  upon  their  degree  of 
curvature,  the  deviation  of  a  ray  of  light  passing  through  them 
being  greater  in  the  double  than  in  the  plano-convex  lens. 

In  order  to  exhibit  the  laws  of  refraction  in  convex  lenses, 

Let  M  N,  Fig.  308,  be  a  double  convex  lens,  P  a  luminous 

Fig.  308. 


TSf 

point  in  the  axis,  A  B,  so  placed  that  the  rays  falling  upon  the 
lens  will  be  rendered  convergent  and  meet  the  axis  at  D,  at  an 
equal  distance  on  the  other  side  of  the  lens.  If  the  radiant  be  re- 
moved to  C,  the  rays  will  be  collected  at  G  ;  that  is,  as  the  radi- 
ant approaches  the  lens,  the  focal  point  recedes.  On  the  other 
hand,  if  the  radiant  be  removed  beyond  P,  the  rays  will  be  col- 
lected at  points  nearer  the  lens  than  D ;  and  if  the  radiant  be 
removed  to  such  a  distance  that  the  rays  are  parallel,  then  they 
will  be  collected  into  a  point  called  the  principal  focus.  We 
may  "determine  the  relative  distances  of  the  focal  point  and  the 
point  P  in  the  following  manner : 

Let  the  radiant  be  so  placed  at  P  that  the  rays  shall  converge 
to  D,  at  an  equal  distance  from  the  lens ;  make  the  angle  P  M  F 
equal  to  F  P  M,  then  the  line  P  F  will  be  equal  to  F  M  ;  and 
as  the  angles  of  deviation  of  two  rays,  F  M  and  P  M,  are  equal, 
the  angle  D  M  H  will  be  equal  to  P  M  F  or  M  D  F,  the  line 
P  M  being  equal  to  M  D  ;  hence  the  ray  M  H  will  emerge  par- 
allel to  the  axis,5*  and  F  is  the  focus  of  parallel  rays. 

Now,  when  the  rays  are  very  near  the  axis,  F  M  and  F  E 
may  be  regarded  as  equal  to  each  other  ;  P  is  therefore  twice  the 

*  For  when  two  lines,  as  M  H  and  F  D,  are  cut  by  a  third  line,  M  D, 
making  the  alternate  angles  equal,  the  two  lines  will  be  parallel. 

Describe  the  action  of  a  double  convex  lens  upon  rays  of  light.  Illustrate 
the  mode  of  determining  the  focus  of  parallel  rays.  How  far  is  it  from 
the  lens  ? 


CONCAVE    LENSES.  353 

distance  of  F  from  the  lens.  The  principal  focus,  or  focus  of  par- 
allel rays,  is  F  ;  and  hence,  if  the  radiant  be  placed  at  tiuice  the 
distance  of  the  principal  focus  of  a  convex  lens,  the  rays  will  con- 
verge to  a  focus  at  an  equal  distance  on  the  other  side  of  the  lens. 
If  the  radiant  be  moved  from  the  focus,  F,  toward  the  lens, 
the  rays  will  not  converge  to  a  focus,  but  will  emerge  diverging, 
though  their  divergency  will  be  less  than  before  refraction. 

The  focal  distance  will  depend  upon  the  form  of  the  lens,  and 
also  upon  its  index  of  refraction.  In  a  double  convex  lens,  the 
curvature  of  whose  surfaces  has  an  equal  radius,  and  whose  index 
of  refraction  is^f ,  the  focus  is  found,  by  experiment,  at  the  center 
of  the  spherical  segments  which  form  the  lens. 

If  the  index  of  refraction  is  greater  than  f ,  the  focus  will  be 
nearer  ;  if  less  than  f ,  more  remote. 

In  a  plano-convex  lens,  whose  index  of  refraction  is  f ,  the 
focus  is  at  a  distance  equal  to  twice  the  radius  of  curvature. 

2.  Concave  Lenses. — Concave  lenses  act  upon  light  in  a  man- 
ner exactly  the  reverse  of  convex  lenses ;  that  is,  they  separate 
the  rays  of  light,  causing  parallel  rays  to  diverge,  diverging  rays 
to  diverge  more,  and  converging  rays  to  converge  less  than  before. 
Fig.  309.  (1.)  Thus,  let  A  B,  Fig. 

A  309,  be  a  double  concave 

lens,  and  let  the  rays  of 
light,  e,  k,  c,  fall  upon  it, 
parallel  to  the  axis,  D  E. 
After  refraction  at  the  two 

B  surfaces,  they  will  diverge 

as  if  they  came  from  the  focal  point,  F. 

(2.)  If  the  radiant  be  brought  toward  the  lens,  the  rays,  after 
refraction,  will  emerge  still  more  divergent ;  and  the  nearer  the 
radiant,  the  nearer  the  imaginary  focus,  F,  will  be  to  the  lens. 

(3.)  If  the  rays  converge  toward  the  focus,  F,  as  y  z,  v  u,  they 
will  emerge,  after  refraction,  parallel  with  the  axis. 

At  what  distance  from  the  lens  will  rays  of  light  radiating  from  a  point  in 
the  axis  be  brought  to  a  focus  ?  What  is  the  distance  of  the  focus  in  a 
double  convex  lens  ?  plano-convex  lens  ?  How  do  concave  lenses  act  upon 
light  ?  Illustrate  the  manner  in  which  rays  of  light  are  refracted  by  a  double 
concave  lens. 


354  NATURAL    PHILOSOPHY. 

(4.)  If  the  rays  converge  toward  a  point  farther  from  the  lens 
than  the  focus,  F,  they  will  be  rendered  diverging. 

(5.)  If  to  a  point  nearer  the  lens  than  the  point  F,  they  will 
converge  less  than  before,  and  meet  the  axis  at  some  point  farther 
than  this  focus  from  the  lens. 

3.  Secondary  Axes. — In  the  cases  above  considered,  both  of 
convex  and  concave  lenses,  the  rays  are  supposed  to  be  parallel 
to  the  axis,  to  radiate  from  or  converge  to  some  point  in  the  axis 
of  the  lens ;  but  there  may  be  an  indefinite  number  of  secondary 
axes,  which  are  the  central  rays  of  each  pencil,  and  these  cut  the 
principal  axis  in  the  optical  center  of  the  lens. 

Thus,  let  M  N,  Fig.  310,  be  a  double  convex  lens,  A  B  the 

mg.  310. 


B 


principal  axis,  any  pencil  of  rays  proceeding  from  any  point  with- 
out this  axis,  as  from  G,  and  falling  upon  the  lens,  will  converge 
to  F' ;  the  axis  of  this  pencil  will  cut  the  principal  axis  in  C, 
and  all  rays  which  pass  through  this  point,  both  in  convex  and 
concave  lenses,  will  be  refracted  in  such  a  manner  that  the  in- 
cident ray,  G  C,  and  the  emergent  ray,  C  F',  will  always  be 
parallel  to  each  other. 

In  order  to  determine  the  position  and  character  of  the  images 
which  may  be  formed  by  means  of  lenses,  it  is  only  necessary  to 
apply  the  principles  already  established. 

4.  Images  of  Convex  Lenses. — Convex  lenses  form  inverted 
images  of  objects. 

Thus,  let  M  N,  Fig.  311,  be  a  double  convex  lens,  A  B  its 
principal  axis,  and  C  D  an  arrow  placed  beyond  the  principal 
focus,  F.  The  pencil  of  rays  emanating  from  C  will  be  collected 
in  G,  and  that  from  D  will  be  collected  in  E,  and  those  which 
proceed  from  the  points  between  C  and  D  will  be  collected  in 

What  are  secondary  axes  ?  Illustrate  the  manner  of  the  formation  of  im- 
ages by  convex  lenses. 


IMAGES  OF  CONVEX  LENSES.  355 

corresponding  points  between  G  and  E  ;  hence  G  E  will  be  an 

E 


inverted  image  of  the  object.  The  reason  for  this  inversion  is, 
that  the  axis  of  each  pencil  must  cross  the  principal  axis  in  the 
optical  center  of  the  lens,  as  C  G  and  D  E. 

The  size  of  the  image,  and  its  distance  from  the  lens,  will  de- 
pend upon  the  distance  of  the  object. 

(1.)  If  the  object  is  twice  the  focal  distance  of  the  lens,  the 
image  will  be  of  the  same  magnitude,  and  at  the  same  distance 
from  the  lens. 

(2.)  If  the  object  approach  the  focus,  the  image  will  recede 
and  increase  in  size  ;  and  when  the  object  arrives  at  the  focus, 
the  image  will  be  at  an  infinite  distance,  as  the  rays  will  then  go 
out  parallel  to  each  other. 

(3.)  If  the  object  be  removed  further  than  twice  the  focal  dis- 
tance, the  image  will  be  nearer  the  lens  than  the  object,  and  less 
in  size  ;  hence 

The  size  of  the  object  is  to  that  of  the  image  as  the  distance 
of  the  object  from  the  lens  is  to  the  distance  of  the  image  from 
the  lens. 

It  will  be  seen  to  follow  from  this  law  that  lenses  of  short 
focal  distances  will  give  images  nearer  the  lens,  and,  consequent- 
ly, smaller  than  those  which  have  a  longer  focal  distance  ;  and 
that,  at  equal  distances  from  the  lens,  the  images  will  be.  larger 
in  proportion  as  the  focal  distance  is  shorter. 

(4.)  If  the  object  be  placed  nearer  the  lens  than  the  focus,  no 
convergent  image  can  be  formed,  because  the  rays  are  in  this  case 

Upon  what  will  the  size  of  the  image  depend  ?  What  ratio  will  the  im- 
age bear  to  the  object  ?  Why  is  the  image  enlarged  ?  What  will  be  the 
effect  if  the  object  is  placed  nearer  to  the  lens  than  the  focus? 


356 


NATURAL    PHILOSOPHY. 


rendered  diverging,  and  yet  ?^- 3i'~- 

they  are  less  diverging  than 
before  refraction  ;  and  hence 
to  an  eye  on  the  other  side 
of  the  lens,  M  N,  Fig.  312, 
the  object  A  B  appears  to 
be  magnified,  erect,  and  fur- 
ther from  the  lens,  as  C  D  ; 
hence  all  objects  seen  through  a  double  convex  lens,  placed  nearer 
than  the  principal  focus,  are  larger  ;  or,  if  the  eye  be  placed  nearer 
the  lens  than  the  principal  focus,  objects,  for  the  same  reason,  will 
be  magnified.  This  is  the  principle  of  the  microscope.  The  ob- 
ject appears  larger,  because  the  lens,  by  causing  the  rays  to  con- 
verge, increases  the  angle  of  vision,  which  is  the  angle  made  by 
two  lines  coming  from  the  extremities  of  the  object  and  meeting 
in  the  eye.  Thus,  an  eye  at  E,  in  Fig.  312,  would  perceive  the 
object  A  B  under  the  enlarged  angle  C  E  D  ;  and  hence  it  would 
be  magnified. 

5.  Images  of  Concave  Lenses. — As  concave  lenses  cause  ray» 
of  light  to  diverge,  they  do  not  give  convergent  images  of  objects  ; 
but,  on  looking  through  such  lenses,  we  see  erect,  diminished  im 
ages.     The  reason  of  this  is,  they  diminish  the  angle  under  which 
the  object  is  viewed. 

Thus,  let  M 
N,  Fig.  313,  be 
a  double  concave 
lens,  and  C  D  an 
arrow.  On  look- 
through  the  lens 
from  E,  all  the 
rays  of  light  from 
the  arrow  will  be  rendered  diverging,  and  appear  to  come  from 
A  B,  which  will  therefore  be  a  diminished  image  of  C  D. 

Concave  lenses  and  convex  mirrors  give  images  smaller  than 
the  objects,  while  convex  lenses  and  concave  mirrors  yield  en- 
larged images  of  the  objects  placed  before  them. 

6.  Spherical  Aberration  of  Lenses. — In  convex  lenses  as  in 
concave  mirrors,  in  order  to  form  a  distinct  image,  the  rays  of 
light  must  be  very  near  the  axis  of  the  lens ;  for,  from  the  laws 


Fig.  313. 


How  are  images  formed  by  concave  lenses  ?     Illustrate  spherical  aberra- 
tion. 


DECOMPOSITION    OF    LIGHT.  3.77 

of  refraction,  in  all  cases  any  two  rays  which  meet  the  axis  at  the 
same  point  must  be  equally  distant  from  the  surface  of  the  lens. 
Those  rays,  therefore,  which  fall  farther  from  the  axis  will  be 
collected  at  points  farther  from  the  optical  center  of  the  lens  than 
those  near  the  point  where  the  axis  meets  it ;  hence,  in  the  pen- 
cils of  light  from  any  object,  the  rays  which  fall  upon  the  surface 
of  a  convex  lens  will  not  all  be  converged  to  the  same  point  in  the 
axis  of  the  pencil.  This  is  called  spherical  aberration  of  lenses. 
The  distance  over  which  the  rays  are  spread  depends  upon  the 
form  and  thickness  of  the  lens,  and  may  be  remedied  by  giving 
the  lens  "  the  form  of  a  spheroid,  whose  major  axis  is  to  the  dis- 
tance between  its  foci  as  the  sine  of  incidence  to  the  sine  of  refrac- 
tion." Rays  parallel  with  this  axis  will  meet  in  the  remoter  focus. 
7.  Burning  Glasses. — Convex  lenses  and  concave  mirrors  not 
only  collect  the  rays  of  light,  but  also  those  of  heat  into  a  focal 
point ;  and  hence  they  are  called  burning  glasses. 

Fig.  314  represents  a  double 
convex  lens,  through  which  the 
rays  of  heat  from  the  sun  are  made 
to  pass,  and  are  converged  by  it  to 
a  focus.  The  degree  of  heat  will 
depend  upon  the  diameter  of  the 
lens,  and  may  be  sufficient  to  melt 
the  most  refractory  substances.  A 
lens  3  feet  in  diameter  has  been 
known  to  melt  cornelian  in  75  sec- 
onds, and  a  piece  of  white  agate  in 
30  seconds. 

IV.  Decomposition  of  Light. — 1.  When  a  beam  of  solar  light 
is  passed  through  a  prism,  it  is  not  only  refracted  at  the  two  sur- 
faces, but  separated  into  seven  differently  colored  rays.  Thi* 
fact  may  be  shown  experimentally  by  admitting  a  beam  of  light 
into  a  darkened  room  through  a  small  orifice  in  the  window 
shutter,  and,  after  passing  it  through  a  prism,  receiving  the  im- 
age upon  a  screen  or  apposite  wall  of  the  room. 

How  may  spherical  aberration  be  remedied  ?  What  are  burning  glasses  ? 
What  is  the  composition  of  light  ? 


358 


NATURAL    PHILOSOPHY. 


Thus,  let  m,  Fig. 
315,  be  a  mirror  to  re- 
flect a  beam  of  light 
from  the  sun  through 
an  aperture,  O,  in  the 
shutter  of  a  darkened 
room.  There  will  be 
formed  a  circular  im- 
age of  the  sun,  directly 
opposite  the  aperture, 
upon  the  screen,  S  r. 

If  now  we  intercept 
the  beam  by  a  triangular  prism,  P,  it  will  refract  the  beam,  and, 
instead  of  the  white  spot,  we  shall  have  a  long,  variously-colored 
surface,  called  the  Solar  Spectrum. 

If  the  beam  is  very  small,  we  may  distinguish  seven  differently- 
colored  surfaces  or  images  of  the  sun  upon  the  screen,  arranged 
as  in  Fig.  315,  red,  orange,  yellow,  green,  blue,  indigo,  and  vio- 
let. The  red  image  is  always  nearest  the  white  light,  and  the 
violet  the  farthest  from  it.  The  red  ray,  therefore,  suffers  the 
least,  and  the  violet  the  greatest  deviation,  while  the  other  colors 
are  intermediate  between  these  two  extremes  ;  that  is, 

2.  The  differently-colored  rays,  are  unequally  refrangible. 
If  each  ray  was  equally  refracted,  we  should  have  simply  an  im- 
age of  white  light,  which,  as  we  have  seen,  Fig.  278,  p.  330, 
would  be  of  the  same  form  as  the  object  which  emits  the  rays — 
in  this  case,  an  image  of  the  sun  ;  and  hence  the  solar  spectrum 
must  consist  of  seven  differently-colored  images  of  the  sun,  which 
slightly  overlap  each  other,  as  represented  in  Fig.  315.  By 
making  the  opening  J^th  of  an  inch  in  diameter,  the  refracting 
angle  of  the  prism  60°,  and  placing  the  screen  18  feet  from  the 
opening,  the  several  colors  are  nearly  distinct.  The  smaller  the 
Jjeam,  the  purer  the  colors  will  appear.  These  colored  bands  are 
not  equal  in  diameter.  If  we  divide  the  spectrum  into  360  equal 
parts,  45  will  be  red,  27  orange,  48  yellow,  60  green,  60  blue, 
40  indigo,  and  80  violet.  These  numbers,  however,  vary  with 
the  substance  of  the  prism.  «, 


How  is  light  decomposed  ? 
spectrum  ? 


How  are  the  colors  arranged  in  the  solar 


THE    SOLAR    SPECTRUM.  359 

To  observe  these  colors,  it  is  only  necessary  to  look  through 
a  prism  upon  external  objects,  or  even  at  the  sky,  when  they  will 
be  seen  in  the  same  order  as  exhibited  upon  the  screen. 

3.  White  light,  then,  consists  of  seven  colors,  each  one  of 
which  is  simple. 

(I.)  That  each  of  the  colored  rays  is  simple,  that  is,  not  com- 
pounded of  two  or  more  colors,  may  be  proved  by  the  following 

Exp. — Pass  a  ray  of  white  light  through  a  prism,  and  then  separate  one 
of  the  colors  by  means  of  a  small  slit  in  a  screen,  or  by  reflection  from  a 
mirror,  and  pass  this  isolated  ray  through  a  second  prism.  The  ray  will 
be  refracted  as  before,  but  will  suffer  no  change  of  color. 

Simple  light  was  called  by  Newton  homogeneous  light. 
(2.)  That  white  light  consists  of  seven  simple  colors,  may  be 
shown  by  passing  these  colors,  in  the  same  proportion  in  which 
they  exist  in  the  solar  spectrum,  through  a  second  prism  with  its 
refracting  angle  inverted.  The  rays  will  then  be  recomposed, 
and  form  a  perfectly  white  image. 

Fig.  316.  Thus,  let  the  two  prisms, 

S  A  A'  and  S'  B  B',  Fig. 
316,  be  so  arranged  that 
the  refraction  of  the  first 
shall  be  exactly  counteract- 
ed by  the  second.    We  shall 
then  have  at  M  a  white  im- 
age, the  same  as  would  be 
U    formed  without  the  prisms. 
(3.)  Newton  further  confirmed  this  fact  by  passing  a  beam  of 
light,  after  it  had  been  decomposed  by  a  prism,  through  a  double 
convex  lens,  and  producing  an  image  of  perfectly  white  light. 

(4.)  Muncfwiv  attached  clock-work  to  the  prism,  so  as  to  give 
it  a  rapid  motion.  By  this  arrangement  the  solar  spectrum  was 
made  to  move  rapidly  back  and  forth  upon  the  screen.  The  im- 
age then  became  white,  slightly  colored  at  the  two  extremities. 
By  this  means  the  different  colors  are  so  mixed  that  the  eye  fails 
to  distinguish  them,  and  the  result  is  a  sensation  of  whiteness. 

(5.)  A  similar  effect  may  be  -produced  by  taking  a  circular 
card,  dividing  it  into  seven  sections  in  the  proportion  in  which 

What  is  the  proof  that  white  light  consists  of  seven  simple  colors  ?  Men- 
tion the  experiments  of  Newton — of  Munchow  ? 


360  NATURAL    PHILOSOPHY. 

the  rays  exist  in  the  solar  spectrum,  and  then  painting  them  as 
nearly  as  possible  with  the  seven  prismatic  colors.  On  causing 
the  card  to  revolve  rapidly  the  separate  tints  will  disappear,  and 
a  grayish- white  light  will  be  reflected  from  its  surface.  If  the 
colors  applied  were  pure  or  simple,  perfectly  white  light  Fig.  317. 
would  be  the  result. 

4.  Fixed  Lines  in  the  Spectrum. — The  solar  spec- 
trum appears  to  be  wholly  colored  when  viewed  at  a 
little  distance  ;  but  when  examined  by  a  microscope,  it 
is  found  to  be  crossed  by  dark  lines,  which  are  constant 
in  position  and  magnitude  when  the  same  kind  of  prisrn 
is  used,  and  the  same  kind  of  light,  but  vary  slightly 
when  the  light  is  separated  by  different  media.     Solar, 
stellar,  and  artificial  lights  have  each  a  different  system. 
Some  of  the  larger  lines  are  represented  in  Fig.  317, 
and  as  they  are  fixed,  they  were  represented  by  Fraun- 
hofer  by  the  letters  of  the  alphabet,  commencing  with 
A  in  the  red. 

5.  Illuminating  Power  and  other  Properties  of  the  Simple 


(1.)  The  several  colored  rays  have  been  found  to  differ  in  their 
illuminating  power.  The  yellow  rays  are  the  most  brilliant ; 
that  is,  yellow  impresses  the  eye  more  powerfully  than  any  other 
color.  This  power  diminishes  gradually  each  way  toward  the 
red  and  violet.  , 

(2.)  It  has  been  found,  also,  that  the  yellow  rays  exert  a  spe- 
cific influence  upon  vegetation,  giving  rise  to  the  green  color  of 
the  leaves  and  other  parts  of  plants. 

(3.)  The  blue  rays  effect  chemical  changes  in  certain  com- 
pounds, especially  in  the  iodides  and  chlorides  of  silver,  substances 
which  are  employed  for  producing  photographic  pictures.  The 
more  refrangible  rays  are  also  concerned  in  producing  phosphor- 
escent light  in  bodies  capable  of  yielding  it.  It  has  been  sup- 
How  can  the  same  effect  be  produced  by  painting  a  card  with  the  pris- 
matic colors  ?  Are  there  any  dark  lines  in  the  spectrum  ?  how  are  they 
designated  ?  Which  rays  possess  the  greatest,  and  which  the  least  illu- 
minating power?  What  rays  influence  vegetation  and  produce  chemical 
changes  ? 


COMPLEMENTARY    COLORS.  361 

posed  that  there  were  toward  the  violet  end  of  the  spectrum  rays 
different  from  those  of  color,  which  are  effective  in  producing 
chemical  changes;  and  hence  they  have  been  termed  chemical 
rays. 

(5.)  Solar  light  is  always  accompanied  by  heat  or  calorific 
rays.  These  rays  are  less  refrangible  than  those  of  color ;  and 
hence  the  greatest  heat  is  found  in  and  near  the  red  rays,  and,  in 
some  cases,  quite  out  of  the  spectrum,  dependent  upon  the  sub- 
stance of  the  prism.  The  intensity  of  the  rays  of  heat  diminishes 
rapidly  toward  the  violet. 

6.  Complementary  Colors. — One  color  is  said  to  be  comple- 
mentary to  another  when  their  union  will  produce  white  light. 

When  the  simple  colors  are  united  in  proper  proportions  they 
produce  white  light  ;  but  if  one  color,  as  red,  is  wanting,  the  re- 
maining colors  will  yield  a  bluish  tint,  to  which  red  is  comple- 
mentary. Each  color  has  its  complementary  color  or  colors,  by 
the  addition  of  which  white  light  will  be  produced. 

For  experiments  on  this  subject,  the  apparatus  represented  in 
Fig.  sis.  Figure  318  may 

be  employed.  It 
consists  of  several 
plane  mirrors  with 
screens,  mounted 
upon  a  frame,  so 
that  any  two  or  more  rays  of  homogeneous  light  may  be  isolated 
and  reflected  to  the  same  spot  on  a  screen.  By  this  means  the 
resulting  colors  may  be  clearly  observed.  Thus, 

Exp. — If  the  red  and  blue  rays  are  reflected  to  the  same  spot,  they  will 
yield  a  purple  image.  Red  and  yellow  will  form  an  orange,  and  yellow 
and  blue  a  green  tint,  to  which,  if  the  remaining  colors  in  each  case  are 
added,  white  light  will  be  produced. 

Some  opticians,  as  Dr.  Brewster,  have  considered  the  solar 
spectrum  to  consist  of  but  three  simple  colors,  red,  yellow,  and 
blue,  and  that  the  other  colors  are  produced  by  their  combination. 

This  theory  supposes  that  some  of  the  red  rays  extend  to  the 

Where  are  the  rays  of  heat  found  ?  What  are  complementary  colors  ? 
Of  how  many  colors  does  the  solar  spectrum  consist,  according  to  Dr. 
Brewster  ? 

Q 


362  NATURAL    PHILOSOPHY. 

violet,  and  also  a  portion  of  the  yellow  and  blue  rays,  though  each 
is  most  intense  in  certain  portions  of  the  spectrum.  Whether 
this  theory  be  true  or  not,  it  is  easy  to  compound  these  three  col- 
ors in  such  proportions  as  to  produce  nearly  every  variety  of  tint. 

7.  Natural  Color  of  Bodies. — If  we  look  through  a  prism 
upon  any  colored  object  we  shall  be  able  to  analyze  the  color 
which  it  reflects. 

Thus,  if  we  take  several  narrow  strips  of  colored  paper — such 
as  is  used  by  bookbinders  for  the  titles  of  books  is  the  best — white, 
scarlet,  orange,  yellow,  green,  and  blue,  and,  having  arranged 
them  near  each  other,  observe  them  through  a  prism,  we  shall 
find  that  the  white  paper  will  yield  all  the  prismatic  colors.  The 
yellow  paper  will  exhibit  colors  nearest  to  the  perfect  spectrum, 
being  wanting  only  in  blue  and  violet,  which,  of  course,  are  com- 
plementary to  it.  The  orange  yields  a  much  less  perfect  spec- 
trum^ because  the  green,  violet,  and  blue  rays  are  wanting.  The 
scarlet  appears  almost  purely  red,  a  slight  tint  of  orange  only  being 
separated ;  while  the  green  and  blue  strips  are  almost  entirely 
deficient  in  red  rays.  The  light  which  is  thus  decomposed  is  that 
which  is  reflected  from  the  body  ;  hence 

The  different  colors  of  natural  objects  depend  upon  the  power 
of  their  surfaces  to  reflect  certain  rays  and  to  absorb  others.  Few- 
bodies,  however,  have  the  power  to  absorb  or  to  reflect  all  the 
rays  of  the  spectrum,  or  of  any  color  which  may  fall  upon  them. 
Objects  which  are  bright  scarlet  absorb  all  but  the  red  and  a 
portion  of  the  orange  rays ;  those  which  are  white  reflect  all  the 
rays  ;  and  those  that  appear  black  absorb  them  all ;  but  most 
colored  objects  absorb  a  portion  of  all  the  rays,  and  reflect  a  por- 
tion of  them ;  hence  we  rarely  see  pure  prismatic  tints. 

It  is  this  power  of  absorbing  and  reflecting  the  different  colored 
rays  of  light  which  gives  to  each  object  in  nature  its  distinctive 
color.  Color,  therefore,  is  a  property  of  light,  but  not  of  matter. 
Material  bodies  only  decompose  the  light,  and  reflect  those  rays 
which  give  them  their  color,  while  the  complementary  colors  are 
absorbed. 

How  may  the  natural  colors  of  bodies  be  analyzed?  On  what  does  the 
color  of  natural  objects  depend  ?  What  gives  a  body  its  distinct  ive  color  7 


CHROMATIC    ABEREATION.  363 

Colored  media  may  be  employed  to  separate  the  rays  of  light, 
those  rays  only  being  transmitted  which  are  of  the  color  of  the 
substance  used,  while  the  other  colors  are  absorbed.  Either  col- 
ored glass  or  colored  infusions  may  be  used  for  this  purpose. 

8.  Chromatic  Aberration. — The  action  of  lenses  upon  light  is 
the  same  as  that  of  prisms  ;  that  is,  when  white  light  is  passed 
through  a  lens  it  is  decomposed.  As  the  red  rays  are  less  refran- 
gible than  the  violet,  they  will  be  brought  to  a  focus  in  a  convex 
lens  farther  from  the  lens ;  and  hence  we  shall  have  a  colored 
image,  so  that  objects  seen  through  lenses  will  be  fringed  with 
the  several  prismatic  colors. 

F&.319.  To  illustrate  this, 

let  A  B,  Figure  319, 
be  a  piano  -  convex 
lens,  through  which 
a  beam  of  light,  par- 
allel to  the  axis,  is 
made  to  pass.  The 
rays  will  be  separa- 
ted ;  the  red  will  ap- 
pear at  r,  and  the 
violet  at  v.  The  space  r  v  is  the  chromatic  aberration  of  the  lens. 
This  property  of  lenses  was  supposed  by  Newton  to  be  incapa- 
ble of  any  remedy  ;  but,  since  his  day,  lenses  have  been  construct- 
ed which  almost  entirely  obviate  the  difficulty.  The  principle 
upon  which  chromatic  aberration  is  avoided  is  founded  in 

The  different  dispersive  powers  of  substances  whose  indices  of 
refraction  are  nearly  equal. 

The  power  which  a  prism  or  lens  has  of  separating  the  colored 
rays  is  called  its  dispersive  power. 

Some  substances  possess  this  power  in  a  much  higher  degree 
than  others.  Thus,  flint  glass  will  separate  the  rays  nearly  twice 
as  far  as  crown  glass,  and  three  times  as  far  as  water  ;  and 
hence  the  breadth  of  its  spectrum,  and,  of  course,  its  dispersive 
power,  will  be  in  the  same  ratio.*  But  the  indices  of  refraction 

*  The  dispersing  power,  however,  is  great  in  proportion  to  the  difference 
between  the  indices  of  refraction  in  the  red  and  violet  rays.  Thus,  in  wa- 

What  is  chromatic  aberration,  and  on  what  principle  may  it  be  avoided  ? 
What  is  meant  by  the  dispersive  |fcwer  of  a  prism  or  lens  ? 


364 


NATURAL    PHILOSOPHY. 


(see  p.  347)  in  crown  and  flint  glass  are  nearly  equal,  being  T53 
in  the  former,  and  1'584  in  the  latter. 

If  now  we  combine  these  two  kinds  of  glass — a  piece  of  flint 
glass,  which  has  twice  the  dispersive  power,  with  a  piece  of  crown 
glass,  whose  refracting  angle  is  made  twice  as  great,  and  there- 
fore has  the  same  dispersive  power,  but  in  an  opposite  direction — 
we  may  wholly  counteract  the  separation  of  the  rays. 

Thus,  let  ABC,  Fig.  320,  be  a  prism  1^.320. 

of  crown  glass,  and  A  C  D  a  prism  of  flint  A D 

glass ;    let  the  refracting  angle  A  C  D  be  A    / 

but  half  that  of  B  AC,  and  let  a  beam  =====7^p*^a^ 
of  light  be  passed  through  this  compound         /      y        assaa*s^ 
prism.  B          C 

It  will  be  seen  that  the  crown  glass,  whose  angle  of  refraction 
is  twice  that  of  the  flint,  has,  on  this  account,  a  dispersive  power 
just  equal  to  it.  It  will,  therefore,  disperse  the  rays  in  the  di- 
rection of  B  C  just  as  far  as  the  flint  glass  will  disperse  them  in 
the  direction  of  A  D,  and  thus  the  dispersive  powers  of  the  two 
glasses  exactly  counteract  each  other,  and  we  shall  have  an  im- 
age of  white  light ;  but  because  the  crown  glass  has  twice  the 
refracting  angle  of  the  flint,  it  will  cause  the  beam  to  deviate  to- 
ward B  C  twice  as  far  as  the  flint  glass  will  in  the  opposite  direc- 
tion, so  that  the  beam  will  still  Fig.  321.  Fig.  322. 
suffer  considerable  deviation  in 
passing  through  the  prism. 

By  applying  this  principle  to 
lenses,  they  are  rendered  achro- 
matic. This  is  done  by  using 
a  convex  lens  of  crown,  and  a 
concave  lens  of  flint  glass,  Fig. 
321,  the  curvatures  of  which 
correspond  to  the  angles  of  the 
prism  in  the  preceding  diagram, 

ter,  the  index  of  refraction  of  the  red  ray  is  1-330,  that  of  the  violet  1-344 ; 
the  difference  being  0-014.  In  flint  glass  the  index  of  refraction  in  the  red 
ray  is  1-628,  and  the  violet  1-671 ;  the  difference  is  0-043,  or  a  little  more 
than  three  times  that  of  water. — Muller. 

How  are  lenses  rencro*ed  achromatic  ? 


EXPLANATION    OF    THE    RAINBOW.  365 

the  curvature  of  the  crown  glass  being  greater  than  the  flint. 
Sometimes  two  double  convex  lenses  of  crown  glass  are  combined 
with  a  double  concave  lens  of  flint  glass,  in  which  case  the  curva- 
tures may  be  exactly  fitted  to  each  other,  Fig.  322. 

Rays  of  light  passing  through  such  lenses  will  converge  to  a 
focal  point  without  dispersion.  It  is  found  difficult,  however,  in 
practice  to  produce  perfect  achromatism;  and  the  best  lenses  give 
a  slight  tinge  of  color  to  the  objects  which  are  seen  through  them. 
V.  Application  of  the  laws  of  refraction  and  of  reflection  to 
the  explanation  of  natural  phenomena. 

There  are  certain  appearances  in  nature  which  are  of  great 
beauty  and  sublimity,  that  find  a  ready  explanation  by  the  prop- 
erties of  light,  which  have  been  hitherto  considered,  such  as  the 
rainbow,  twilight,  spectral  apparitions,  mirage,  &c. 

1 .  The  Rainbow. — The  rainbow  is  one  of  the  most  beautiful 
and  striking  phenomena  in  the  natural  world.  It  consists  of  one 
or  more  broad  circular  arcs  of  the  prismatic  colors  painted  upon  the 
surface  of  the  sky,  opposite  the  sun.  The  bow  is  seen  when  the 
back  is  turned  toward  the  sun,  and  forms  the  base  of  a  cone, 
whose  apex  is  the  eye,  and  whose  axis  is  a  line  passing  from  the  sun 
through  the  eye,  and  also  the  center  of  the  circle  of  which  the  bow 
is  an  arc.  In  order  to  understand  how  this  arc  is  formed,  it  is  neces- 
sary to  examine  the  action  of  a  drop  of  water  upon  the  sun's  rays. 
Drops  of  water  have  the  properties  of  a  lens  and  of  a  reflect- 
ing surface. 

Thus,  let  A  H,  Fig.  323,  be 
a  drop  of  water,  S  i  parallel  rays 
of  light  from  the  sun.  These  rays 
will  be  refracted  at  i  to  e,  and 
the  colored  rays  separated.  At 
e  a  portion  of  them  will  be  reflect- 
ed  to/  and  g,  where,  passing  out 
of  the  drop,  they  will  be  again 
refracted  to  o  and  b,  and  an  eye 
placed  at  these  points  will  perceive  the  prismatic  colors,  red,  or- 
ange, yellow,  &c.,  painted  beyond  the  drop,  as  at  a. 

It  will  be  seen  that  all  the  rays  which  are  parallel  when  they 

What  natural  appearances  may  be  explained  by  the  reflection  and  refrac- 
tion of  light  ?  Describe  the  rainbow.  Explain  the  mot>  of  its  production. 


366 


NATURAL    PHILOSOPHY. 


fall  upon  the  drop  will  not  emerge  from  it  parallel ;  and  hence, 
that  the  angles  of  deviation  formed  by  the  incident  and  emergent 
rays,  as  S  a  b,  will  not  all  be  equal  to  each  other. 

Now  it  is  found  that,  of  all  the  rays  which  fall  upon  the  drop, 
only  those  which  emerge  nearly  parallel,  and  make  an  angle  of 
42°  30'  with  the  incident  rays,  will  reach  the  eye,  and  produce 
the  sensation  of  light.  As  the  drops  of  water  are  constantly  fall- 
ing between  the  observer  and  the  place  of  the  bow,  and  rays  of 
light  falling  upon  them,  only  those  drops  which  lie  upon  the  sur- 
face of  a  cone,  the  radius  of  whose  base  subtends  an  angle  of  42° 
30',  will  so  refract  and  reflect  the  light  as  to  reach  the  eye  of  the 
observer. 

To  render  this  more  distinct,  let  O  P,  Fig.  324,  be  a  line 


3 


passing  through  the  sun  and  the  eye,  and  extending  toward  the 
center  of  the  bow,  and  through  this  line  pass  a  vertical  plane. 


SECONDARY    BOW. 

Through  O  draw  the  straight  line  O  C  in  this  plane,  so  that  the 
angle  P  O  C  shall  be  equal  to  42°  30'.  Let  this  plane  be  re- 
volved about  the  axis  P  O ;  then  all  the  drops  which  lie  upon  the 
surface  of  the  cone,  whose  convex  surface  is  described  by  the  line 
O  C,  will  send  emergent  rays  of  light  to  the  eye  of  the  observer 
at  O,  and  hence  he  will  perceive  an  arch  of  colored  light. 

The  arc  of  red  light  will  be  on  the  outer  side  of  the  bow,  and 
will  be  about  30'  in  diameter,  because  the  sun  is  not  a  point,  but 
has  an  apparent  diameter  of  30' ;  the  violet  band  will  be  of  the 
same  width,  but  will  occupy  the  inner  portions  of  the  bow,  be- 
cause these  rays  make  an  angle  of  only  40°  30'  with  the  incident 
rays.  The  width  of  the  bow  will  therefore  be  2°.  The  other 
bands  will  occupy  the  intermediate  space  between  the  red  and 
violet,  as  in  the  solar  spectrum. 

The  position  of  the  arc  will  depend  upon  the  height  of  the  sun 
above  the  horizon. 

When  the  sun  is  in  the  horizon  and  the  observer  at  the  level 
of  the  sea,  the  bow  is  an  exact  semicircle,  with  its  center  in  the 
horizon.  If  the  observer  is  upon  a  mountain,  more  than  a  semi- 
circle will  be  seen.  In  some  cases  a  complete  circle  is  observed, 
especially  at  certain  waterfalls.  If  the  sun  is  above  the  horizon, 
less  than  a  semicircle  is  visible. 

The  altitude  of  the  bow  will  depend  upon  that  of  the  sun. 
The  higher  the  sun  is,  the  lower  the  arc,  until,  at  an  altitude  of 
42°  30',  it  becomes  invisible,  or  sinks  below  the  horizon. 

Secondary  Boiv. — In  addition  to  this  the  primary  bow,  there 
is  generally  a  second  arc,  somewhat  larger,  called  the  Secondary 
Bow,  because  it  was  at  one  time  supposed  to  be  produced  from 
the  first ;  but  it  is  due  to  the  same  laws  of  refraction  and  reflec- 
tion as  the  primary  bow,  and  independent  of  it.  There  is,  how- 
ever, this  difference ;  the  rays  which  form  this  second  arc  are 
not  only  twice  refracted,  but  twice  reflected,  and,  on  this  account, 
the  order  of  the  colors  will  be  exactly  reversed,  and  the  arc  will 
be  situated  exterior  to  the  primary  bow. 

Where  will  the  red  light  be  situated  ?  What  will  be  the  breadth  of  the 
bow,  and  why  ?  Upon  what  will  the  position  and  altitude  of  the  arc  de- 
pend ?  Describe  the  secondary  bow. 


368 


NATURAL    PHILOSOPHY. 


Fig.  325. 


To  illustrate  this,  let  a  ray  of  light 
proceed  from  S,  Figure  325,  and  fall 
upon  a  drop  of  water,  it  will  be  reflect- 
ed at  I',  and  again  at  I"  ;  and,  after 
two  refractions,  as  in  the  primary  bow, 
will  meet  the  eye  if  it  be  properly  situa-  s 
ted. 

In  this  case  the  incident  and  emergent  rays  cross  each  other, 
and  it  is  found  that  those  emergent  rays  which  make  an  angle 
with  the  former  of  about  50°  will  impress  the  eye  with  the  sensa- 
tion of  a  colored  image  or  bow.  The  red  rays  will  be  on  the  in- 
ner portions  of  the  bow,  making  an  angle  of  50°,  while  the  violet 
will  be  on  the  exterior  portion,  making  an  angle  of  53°  30'.  The 
breadth  of  the  bow  will,  therefore,  be  3°  30',  or  1°  30'  broader 
than  the  primary  bow,  but  somewhat  paler,  because  some  rays 
are  lost  at  each  reflection  within  the  drop. 

Similar  bows  are  often  produced  by  the  light  of  the  sun  re- 
flected from  the  moon,  called  Lunar  Bows,  but  they  are  very 
pale  and  indistinct. 

2.  Astronomical  Refraction. — Rays  of  light  passing  obliquely 
through  the  atmosphere  are  more  or  less  bent  from  a  direct 
course,  by  refraction,  toward  a  perpendicular  to  the  surface  ;  and 
hence  the  heavenly  bodies  seen  in  any  other  position  than  in  the 
zenith  are  slightly  elevated. 

To  make  this  evident,  let 
R,  Fig.  326,  be  a  star,  S  O 
S  the  surface  of  the  earth, 
and  a  a,  b  b,  c  c,  successive 
strata  of  air  of  different  densi- 
ty. As  the  ray  from  R  falls 
upon  the  stratum  c  c,  in  the 
direction  R  E,  it  is  bent  out 
of  its  course,  and  still  farther 
deflected  by  the  other  strata, 
until  it  meets  the  surface  of  the  earth  at  O.  Now,  as  all  objects 
are  seen  in  the  direction  in  which  the  light  meets  the  eye,  R  will 
appear  elevated  to  r. 

On  this  account  the  sun's  rays  are  so  refracted  that  we  see  his 

How  do  its  size  and  position  compare  with  the  primary  bow  ?  What 
are  lunar  bows  1  What  is  astronomical  refraction  ?  Illustrate. 


z 

/ 

~~7~ 

•  1^' 

**- 

IE 

O    " 

TWILIGHT HALOS.  369 

whole  disc  before  he  is  above  the  horizon,  and  also  after  he  is 
below  the  horizon  when  he  sets.  On  this  account,  also,  the  day 
in  the  polar  regions  is  nearly  a  month  longer  than  it  would  other- 
wise be. 

The  nearer  the  luminous  body  is  to  the  horizon,  the  greater 
will  be  its  elevation,  because  the  rays  traverse  a  denser  medium. 
This  is  the  reason  that  the  sun  and  moon,  when  in  the  horizon, 
present  an  oval  figure,  the  rays  from  the  lower  parts  of  their  discs 
being  more  refracted  than  those  from  the  upper  parts. 

3.  Twilight. — It  is  evident  that  some  rays  of  light  thus  bent 
out  of  their  course  will  reach  the  earth  where  the  sun  is  below 
the  horizon ;  but,  in  addition  to  this,  the  atmosphere,  with  its 
watery  vapor,  not  only  refracts,  but  reflects  the  light  more  or 
less,  and  by  this  means  gives  rise  to  twilight.     The  degree  of 
light  will  depend  upon  the  distance  of  the  sun  below  the  hori- 
zon.    The  light  gradually  diminishes  till  the  sun  is  18°  below 
the  horizon,  when  it  entirely  ceases.     This  is  the  reason  that 
twilight  is  enjoyed  in  the  northern  regions  for  months ;  the  sun, 
owing  to  the  obliquity  of  his  path  to  the  horizon,  is  for  a  long 
time  less  than  18°  degrees  below  it. 

4.  Halos.    Parhelia .« — We  often  observe,  when  the  sky  is  filled 
with  watery  vapor,  just  before  a  storm,  colored  rings  encircling 
the  sun  and  moon,  which  are  called  halos.     These   are  pro- 
duced by  the  light  falling  upon  the  vapor  or  hollow  vesicles  of 
water,  and  are  accounted  for  by  the  interference  of  the  rays  of 
light,  which  will  be  explained  in  a  future  section.     There  are 
also  two  other  colored  circles,  often  connected  with  bright  spots 
or  streaks  of  light,  called  parhelia,  both  of  which  have  been  ex- 
plained by  supposing  that  small  drops  of  water  are  formed  into 
ice  prisms,  that  partially  decompose  the  light. 

5.  Color  of  the  Sky. — The  blue  color  of  the  sky  may  be  ex- 
plained on  the  principle  that  the  blue  rays  of  light  only  are  re- 
flected to  the  eye  by  the  particles  of  the  atmosphere.     Were  no 

What  effect  has  astronomical  refraction  upon  the  length  of  the  day? 
How  is  twilight  produced,  and  how  does  it  vary  in  length?  What  are 
halos,  and  how  are  they  explained  ?  How  is  the  color  of  the  sky  account- 
ed for-? 


370 


NATURAL    PHILOSOPHY. 


rays  reflected  by  the  atmosphere,  the  color  of  the  sky  would  be 
perfectly  black.  The  color  differs  at  different  times  and  places, 
and 'this  is  due  to  the  condition  of  the  atmosphere,  the  presence 
of  vapor,  or  clouds. 

The  gorgeous  colors  often  witnessed  in  the  evening  and  morn- 
ing sky  are  explained  by  the  fact  that  the  clouds  transmit  or  re- 
flect only  red  and  yellow  rays.  The  evening  sky  is  more  brilliant 
than  the  morning,  owing  to  the  peculiar  condition  of  the  watery 
vapor,  which  at  that  period  is  on  the  point  of  condensation,  while 
in  the  morning  this  vapor  is  condensed,  and  more  rays  are  trans- 
mitted. This  gives  a  grayish  appearance  to  the  sky  ;  but  if  the 
"morning  is  red,"  it  shows  that  great  quantities  of  vapor  are  in 
the  air,  and  a  storm  is  generally  expected. 

6.  Mirage. — In  certain  states  of  the  atmosphere,  when  the 
lower  strata  are  much  rarefied  by  contact  Fig.  327. 

with  the  heated  earth,  inverted  images  of 
Greets  are  often  seen  painted  upon  the 
face  of  the  sky,  near  the  horizon.  Villages 
and  vessels  at  sea  are  sometimes  thus 


Tne  appearance  represented  in  Fig' 
3Z7  was  observed  by  Dr.  Vince  in  1789. 
The  mast  of  a  ship,  A,  was  just  visible  at 
Ramsgate,  and  directly  above  it  two  im- 
ages of  the  same,  B,  C,  one  erect  and  the 
other  inverted. 

This  appears  to  be  due  to  the  extra- 
ordinary refraction  and  reflection  'of  light, 
produced  by  strata  of  unequal  density. 
A  similar  phenomenon  may  be  witnessed 
by  viewing  a  small  object  placed  beyond  a  heated  bar  of  iron. 

The  glimmering  which  is  seen  in  a  hot  day  near  the  surface 
of  the  earth,  and  upon  the  surface  of  bright  objects,  is  also  due  to 
hot  and  cool  currents  of  air,  which  refra<$  and  reflect  the  light  as 
it  passes  through  them. 

What  is  the  cause  of  the  brilliant  colors  of  evening  and  morning  ?  What 
is  mirage,  and  how  is  it  explained  ? 


VISION — ITS  CAUSE.  371 

SECTION  IV.— OF  THE  EYE  AND  OPTICAL  INSTRUMENTS. 

The  sensation  of  light  is  due  to  the  excitement  of  certain 
nerves  which  are  spread  over  the  interior  coat  of  the  eye,  called 
the  retina.  Vision  is  the  perception  of  an  object  by  means  of 
light.  Eyes  are  of  two  kinds. 

I.  Compound  eyes,  such  as  the  eyes  of  most  insects. 

II.  Simple  eyes,  with  convex  lenses,  as  those  of  man  and  other 
vertebrate  animals. 

III.  Simple  eyes  have  the  power  of  perceiving  near  and  dis- 
tant objects,  there  being  certain  limits  beyond  which  objects  be- 
come dim  and  invisible. 

IV.  The  impression  made  by  light  upon  the  organs  of  seme 
remains  a  short  time  after  the  object  is  removed. 

V.  For  the  purpose  of  aiding  the  eye  to  perceive  near  and 
distant  objects,  or  of  presenting  their  magnified  images,  certain 
instruments  have  been  invented,  such  as  the  camera  obscura,  the 
simple,  compound,  and  solar  microscopes,  the  magic  lantern,  and 
refracting  and  reflecting  telescopes. 

1 .  THE  sensation  of  light  is  produced  by  rays  of  light  falling 
upon,  and  thereby  setting  in  motion,  certain  delicate  nerves,  which 
are  distributed  over  the  interior  coat  of  the  eye,  called  the  retina. 
The  sensation  of  darkness  is  experienced  when  these  nerves  are 
at  rest.     There  are,  however,  some  other  causes  which  produce 
this  sensation,  as  a  sudden  blow,  a  rush  of  blood  to  the  brain,  an 
electrical  discharge  near  the  eye,  &c.     But  there  may  be  the 
sensation  of  light  without  vision. 

2.  By  vision  is  meant  the  mind's  perception  of  external  objects 
through  the  medium  of  light.     To  produce  vision,  it  is  necessary 
that  the  object  seen  should  be  accurately  depicted  upon  the  retina. 
In  order  to  this,  a  special  apparatus  is  requisite,  and  this  is  found 
to  be  a  strictly  mechanical  contrivance,  founded  upon  principles 
already  explained.     In  some  animals  this  apparatus  is  wanting, 
and  in  such  cases  they  may  be  able  to  distinguish  light  from 
darkness,  but  can  have  no  perception  of  external  objects. 

How  is  the  sensation  of  light  produced  ?     What  is  vision,  and  by  what 
means  is  it  produced  ? 


372  NATURAL    PHILOSOPHY. 

3.  The  apparatus  by  which  the  rays  of  light  are  made  sub- 
servient to  vision  is  very  diverse  among  the  different  orders  of 
animals ;  but  these  differences  may  be  reduced  to  two — com- 
pound eyes,  as  those  of  most  insects  and  crustaceans,  and  simple 
eyes  ivith  convex  lenses. 

I.  Compound  Eyes. — For  our  knowledge  of  the  structure  of 
this  class  of  eyes,  we  are  indebted  to  the  investigations  of  Miiller. 
He  has  shown  that  such  eyes  consist  of  a  great  number  of  small 
cones,  standing  upon' the  retina  in  such  a  way  that  only  the  light 
from  external  objects  which  is  parallel  with  the  axis  of  each  cone 
can  reach  the  retina,  all  the  other  rays,  falling  upon  the  inner  sur- 
face of  the  eye,  being  absorbed  by  a  dark-colored  pigment  which 
lines  the  sides  of  these  cones.     The  distinctness  of  the  image  de- 
pends upon  their  number. 

The  external  membrane  which  covers  them  is  divided  into 
facettes,  corresponding  to  the  number  of  cones,  which,  in  some 
cases,  amount  to  25,000.  Spiders  have  eyes  with  convex  lenses ; 
some  insects  have  both  kinds  of  eyes. 

II.  Simple  Eyes  with  Convex  Lenses. — Eyes  of  this  kind  be- 
long mostly  to  vertebrated  animals.     The  images  of  .external  ob- 
jects are  formed  on  the  retina  of  such  eyes  in  precisely  the  same 
manner  as  they  are  formed  by  a  double  convex  lens  upon  a  screen. 

Thus,  let  a  c,  Fig.  328,  be  jFV-328. 

an  object,  and  b  b'  b"  the  eye. 
The  rays  of  light  will  pass  into 
it  at  s  s,  and,  after  crossing  ea,ch 
other,  will  be  refracted  by  the 
lenses  of  the  eye,  and  form  an 
inverted  image  upon  the  inner 
membrane  or  retina,  m  n.  The 
whole  formation  of  the  eye  contributes  to  this  effect. 

The  outer  coat  of  the  eye,  called  the  sclerotica,  b  b'  b",  is  a 
strong  membrane,  covering  the  eye  entirely,  with  the  exception 
of  a  small  round  plate  in  front,  bf,  like  the  convex  crystal  of  a 
watch,  which  is  transparent,  and  called  the  cornea,  and  by  which 
the  rays  of  light  begin  to  be  refracted  convergently  on  their  en- 
trance into  the  eye. 

How  many  kinds  of  eyes  are  there,  and  what  are  they  called  ?  Describe 
compound  eyes.  Where  are  such  eyes  found  ?  Describe  simple  eyes  with 
convex  lenses. 


DISTANCE    OF    DISTINCT    VISION.  373 

Immediately  behind  the  cornea  is  the  iris,  which  is  a  thin 
colored  membrane  stretched  directly  across  the  eye,  having  an 
aperture  in  its  center,  s  s,  called  the  pupil.  Through  this  the 
rays  are  admitted  to  the  crystalline  lens,  c  c',  which  lies  directly 
behind  the  iris,  and  by  which  they  are  converged  still  more. 

The  space  between  this  lens  and  the  cornea  is  filled  by  a  clear 
and  somewhat  saline  fluid,  called  the  aqueous  humor ;  and  the 
whole  space  behind  this  lens  is  occupied  by  a  transparent  gelat- 
inous substance,  called  the  vitreous  humor,  both  of  which  exer- 
cise a  converging  refractive  power  upon  light  as  it  passes  through 
them. 

Besides  the  outer  or  sclerotic  coat  there  are  two  other  mem- 
branes. The  one  next  the  sclerotica  is  called  the  choroid,  and 
is  covered  on  its  inner  surface  with  a  black  pigment,  pigment- 
urn  nigrum,  for  the  purpose  of  absorbing  any  rays  which  might 
interfere  with  the  distinctness  of  the  image  formed  on  the  retina. 
The  other  membrane,  lining  the  interior  of  the  eye,  d  d',  is  the 
retina,  upon  which  nerves,  coming  from  the  optic  nerve  o,  are 
spread  to  receive  the  image  m  n,  and  convey  the  sensation  fo  the 
mind. 

That  there  is  an  exact  inverted  image  of  the  object  upon  the 
retina  may  be  proved  by  taking  the  eye  of  an  ox,  and,  after  re- 
moving the  coats  on  the  back  of  it,  inserting  it  in  an  aperture  of 
a  window-shutter  of  a  darkened  room,  when  external  objects  will 
be  seen  by  those  in  the  room,  perfectly  painted  upon  the  retina 
in  the  back  part  of  the  eye.  The  image  will  be  more  distinct 
if  the  eye  of  the  white  rabbit  is  employed,  because  it  is  destitute 
of  pigment. 

III.  Distance  of  distinct  Vision. — As  the  eye  acts  like  a 
lens,  when  the  object  is  near,  the  image  is  more  distant  than 
when  the  object  is  more  remote.  In  order,  therefore,  for  the 
eye  to  see  objects  distinctly  at  different  distances,  it  must  have 
the  power  of  elongating  or  shortening  the  axis  of  the  eye,  or  of 
making  the  lenses  more  or  less  convex. 

1 .  Olbers  has  shown  that,  if  the  curvature  of  the  cornea  were 

Mention  the  several  parts  of  which  the  eye  is  composed,  and  the  forma- 
tion of  images  within  it.  What  is  the  distance  of  distinct  vision? 


374  NATURAL    PHILOSOPHY. 

so  altered  that  its  radius  should  vary  from  '333  to  '300  of  an 
inch,  the  axis  would  be  elongated  about  one  line,  and  this  would 
be  sufficient  to  adapt  the  eye  to  distinct  vision  from  four  inches  to 
infinity.  Thus,  at  an  infinite  distance,  the  image  is  -8997  of  an 
inch  from  the  cornea. 

2.  The  reason  that  objects  at  different  distances  are  seen  dis- 
tinctly may  be  explained  by  compression  and  change  of  position 
of  the  lens ;  but  neither  explanation  rests  upon  positive  certainty 
as  to  the  fact,  and  possibly  both  modes  may  be  employed  to  pro- 
duce the  effect. 

3.  There  is  a  limit  to  distinct  vision,  which  varies  slightly  in 
different  eyes.     The  eye  is  capable  of  accommodating  itself  to 
the  distance  of  an  object,  until  it  is  within  8  or  10  inches ;  and 
then,  if  brought  nearer,  the  eye  is  obliged  to  make  an  effort  to  see 
it,  and  as  it  is  brought  nearer  and  nearer,  it  grows  more  and 
more  dim  until  it  becomes  invisible.     We  involuntarily  hold  an 
object  at  the  distance  of  distinct  vision.     If  this  distance  is  more 
than  8  inches,  we  are  said  to  be  long-sighted,  if  less,  short-sighted. 

4.  When  the  object  is  too  near,  indistinct  vision  is  produced, 
because  the  rays  from  it  fall  so  diverging  upon  the  eye  that  they 
can  not  be  converged  to  a  focus  by  the  time  they  reach  the  retina, 
but  fall  upon  it  in  a  circle,  the  point  where  they  would  be  brought 
to  a  focus  being  just  behind  the  retina.     Thus, 

If  through  two  minute  orifices  in  a  card,  we  look  at  a  pin  head, 
held  very  near  the  eye,  we  shall  see  two  distinct  images  of  it,  be- 
cause the  pencil  of  rays  which  would  be  dispersed  in  a  circle  upon 
the  retina  is  intercepted  by  the  card,  and  only  a  few  rays  reach 
the  retina  at  two  points  of  this  circle.  But  if  the  pin  be  removed 
to  the  distance  of  distinct  vision,  these  two  images  will  be  merged 
into  one.  By  means  of  this  experiment,  instruments  are  con- 
structed called  opt&nieters,  which  enable  us  to  define  the  distance 
of  distinct  vision. 

5.  In  short-sightedness  the  eye  is  too  convex,  and  the  rays  are 
brought  to  a  focus  too  soon.     In  order  to  remedy  this  defect,  con- 
Why  do  very  near  objects  appear  indistinct?     By  what  means  can  the 

eye  accommodate  itself  to  objects  at  different  distances  ?  How  is  short- 
sightedness remedied  ? 


SHORT-SIGHTEDNESS    AND    LONG-SIGHTEDNESS.  375 

cave  glasses  are  used,  which  tend  to  separate  the  rays,  so  that  by 
falling  more  divergent  they  are  not  brought  to  a  focus  before  they 
reach  the  retina. 

Short-sightedness  is  often  produced  by  habitually  holding  the 
object  too  near  the  eye.  It  generally  occurs  in  early  life,  and 
ceases  as  the  eye  is  flattened  by  advancing  age. 

6.  In  long-sightedness  the  eye  is  too  flat,  and  the  rays  are  not 
brought  to  a  focus  soon  enough.     To  remedy  this,  convex  glasses 
are  worn,  which  render  the  rays  so  converging  that  they  may  be 
brought  to  a  focus  on  the  retina.     Aged  people  become  long-sight- 
ed in  consequence  of  the  flattening  of  their  eyes,  and  are  obliged 
to  resort  to  convex  glasses  in  order  to  see  distinctly. 

7.  There  is  another  limit  of  distinct  vision  depending  upon 
the  angle  which  the  object  subtends  to  the  eye.     When  an  ob- 
ject is  situated  at  such  a  distance  that  the  rays  coming  from  its 
two  extremities  make  an  angle  of  2",  it  can  be  distinctly  seen, 
but  if  it  be  less,  it  is  invisible.     All  objects,  therefore,  become  in- 
visible if  they  are  removed  to  a  sufficient  distance ;  hence  the 
apparent  size  of  objects  will  depend  upon  the  angle  at  which 
they  are  seen. 

Fig.  329.  To  illustrate  this,  let  A  C  B, 

Fig.  329,  be  the  angle  under 
which  the  arrows  i  k,  &c.,  are 
seen ;  then  the  arrow  i  k  will 
appear  just  as  large  as  g  h,  eft 
or  those  at  the  distance  A  B. 
B  It  is  on  this  principle  that 
convex  lenses  magnify  objects,  because  they  increase  the  angle 
under  which  they  are  seen. 

8.  The  images  of  all  objects  are  inverted  on  the  retina,  be- 
cause rays  from  the  top  of  the  object  enter  the  pupil  descending, 
and,  continuing  the  same  course,  fall  upon  the  lower  part  of  the 
retina,  and  there  form  their  image,  while  those  from  the  bottom 
enter  the  pupil  ascending,  and,  continuing  their  course  afterward 
in  the  same  direction,  form  their  image  on  the  upper  part  of  the 

How  is  long-sightedness  remedied  ?  What  limit  to  distinct  vision  ?  What 
influence  has  the  angle  of  vision  upon  the  size  of  objects  ?  Why  are  images 
of  objects  inverted  ? 


376  NATURAL    PHILOSOPHY. 

retina.  Why  the  object  is  seen  erect,  since  its  image  id  inverted, 
is  not  easily  explained.  It  is  supposed,  however,  that  the  image 
does  not  exist  as  a  sensation,  but  that  the  mind  projects  it,  as  it 
were,  in  the  direction  in  which  the  rays  come  to  the  eye. 

9.  It  may  be  asked  why,  since  the  image  of  an  object  is 
formed  on  the  retina  of  each  eye,  we  do  not  see  objects  double. 
This  question  has  been  variously  answered.  It  is  supposed  to  be 
owing  to  the  fact  that  the  two  images  fall  upon  corresponding 
parts  of  the  retina,  and  hence  vision  is  single.  If  this  relation 
is  disturbed,  as  it  may  be  by  turning  the  eyes  inward,  two  im- 
ages will  be  formed,  or  vision  will  be  double. 

IV.  Duration  of  the  Impressions  of  Light. — The  sensation  of 
light  does  not  instantly  cease  when  the  object  which  produces  it 
is  removed.     If  a  flaming  torch  be  whirled  rapidly  around,  we 
see  a  circle  of  light.     In  the  rapid  revolution  of  a  wheel  we  are 
not  able  to  distinguish  the  spokes,  because  the  impression  made 
by  one  remains  till  the  next  one  arrives  at  the  same  place,  and 
thus  the  impression  of  a  solid  wheel  is  given.     If  upon  a  green 
card  an  animal,  or  any  figure,  is  painted  in  red,  and  the  card  is 
then  moved  quickly  back  and  forth  before  the  eye,  the  impression 
of  the  red  color  will  remain  upon  the  eye,  and  the  animal  will 
appear  to  move  upon  the  green  ground. 

There  are  many  very  amusing  experiments  in  which  figures 
of  animals  painted  with  different  colors  are  made  to  perform  vari- 
ous evolutions,  all  depending  upon  the  duration  of  the  impression 
of  light. 

V.  Optical  Instruments. — For  the  purpose  of  obtaining  mag- 
nified images  of  objects  near  or  remote,  certain  instruments  have 
been  invented  which  have  greatly  enlarged  our  ideas  of  the  per- 
fection and  greatness,  as  well  as  of  the  minuteness  of  the  works 
of  God. 

1.  The  Camera  Obscura. — If  an  aperture  is  made  in  a  win- 
dow-shutter, and  the  light  from  any  external  object,  as  an  animal 
or  a  tree,  Fig.  330,  is  admitted  into  a  darkened  room,  an  invert- 
Why  do  the  images  appear  erect?  Why  are  not  objects  seen  double  ? 
Does  the  impression  of  light  remain  airy  time  upon  the  retina  ?  How  is  this 
proved  ?  What  is  the  object  of  optical  instruments  ?  Describe  the  camera. 


OPTICAL    INSTRUMENTS. 
Fig.  330. 


377 


ed  image  of  the  object  will  be  painted  upon  the  opposite  wall. 
Such  a  room  is  a  camera  obscura. 

The  manner  in  which  this  effect  is  produced  was  noticed  on 
page  330.  The  rays  of  light  from  the  bottom  of  the  object  pass 
through  the  aperture  and  form  an  image  near  the  top  of  the 
room,  while  those  from  the  top  pass  to  the  bottom  of  the  room, 
the  rays  crossing  each  other  in  the  aperture. 

The  camera,  as  usually 
constructed,  consists  of  a  box, 
M  N,  Fig.  331,  with  a  pro- 
jecting tube,  d,  containing  a 
double  convex  lens,  for  the 
purpose  of  converging  the 
rays  and  more  highly  illumin- 
ating the  image,  and  a  screen  of  ground  glass,  placed  either  on 
the  back  of  the  box  where  the  image  will  be  inverted,  or  upon 
the  top,  as  a  b,  or  bottom,  upon  which  the  image  is  thrown  by 
means  of  a  mirror,  m,  placed  at  an  angle  of  45°,  in  which  case 
the  image  will  be  in  its  natural  position. 

The  form  of  this  instrument  may  vary  to  suit  the  manner  of 
using  it.  If  the  object  is  to  trace  the  picture,  it  is  often  thrown, 
by  a  mirror,  upon  a  sheet  of  paper  in  the  bottom  of  the  box,  and 
there  traced  with  a  pencil.  Natural  scenery  may  thus  be  ac- 
curately represented  and  delineated  upon  paper,  or  indelibly  fix- 
ed on  metallic  plates,  as  in  the  Daguerreotype. 

2.  The  Simple  Microscope. — This  consists  simply  of  a  double 
convex  lens,  and  when  an  object  is  placed  a  little  nearer  than  the 
focal  distance,  and  viewed  through  the  lens,  it  appears  magnified. 


Describe  the  simple  microscope. 


378 


NATUfcAL    PHILOSOPHY. 


Fig.  332. 


Let  the  object,  c  b,  Fig.  332,  c 
be  placed  on  one  side  of  a  double 
convex  lens,  and  be  viewed  by  an 
eye,  a,  on  the  other  side.     The 
ray  from  c  will  be  refracted,  and 
will  enter  the  eye  as  if  it  came 
from  C  ;    and   as   the  object   is 
seen  in  the  direction  of  the  refracted  ray,  it  will  appear  much 
larger  than  it  really  is. 

To  estimate  the  power  of  such  a  lens  of  enlarging  the  dimen- 
sions of  an  object,  we  must  take  into  consideration  the  following 
principle,  alluded  to  above,  that  the  apparent  magnitude  of  an 
object  depends  upon  the  angle  at  which  it  is  vieived;  and  the 
nearer  it  is,  the  greater  is  its  apparent  magnitude.  Thus,  if  the 
focal  length  of  the  glass  in  this  case  is  half  an  inch,  and  the  ob- 
ject is  seen  distinctly,  that  may  be  considered  the  distance  of  the 
object  from  the  eye.  By  comparing  this  with  the  distance  of 
distinct  vision,  8  inches,  it  will  appear  as  much  enlarged  in  any 
one  direction  as  the  distance  of  distinct  vision  is  greater  than  the 
focal  distance  of  the  lens.  The  magnifying  power  of  any  lens 
may  therefore  be  ascertained  by  dividing  the  distance  of  distinct 
vision,  8  or  10  inches,  by  the  focal  distance  of  tKe  lens,  in  this 
case  half  an  inch,  which  will  increase  each  dimension  twenty 
times.  But  this  is  not  strictly  true,  for  the  object  is  not  exactly 
in  the  focus,  and  the  magnifying  power  is  a  little  greater  than 
this  ratio  would  make  it.  It  will  be  seen  that  the  shorter  the 
focal  distance  of  the  lens,  the  greater  is  its  magnifying  power. 

3.  The  Compound  Microscope. — In  this  microscope  there  are 
two,  and  sometimes  three,  lenses.  One  forms  the  object-glass,  as 
A  B,  Fig.  333,  and  one  the  1^.333. 

eye-glass,  as  C  D.  When 
there  is  a  third,  as  E  F,  the 
middle  one  is  called  ihejield- 
glass,  because  it  enlarges  the 
field  of  vision,  by  collecting 
the  rays  that  otherwise  would 
not  fall  upon  C  D.  The  ob- 

Why  does  the  simple  microscope  magnify  objects  ?  How  is  the  magni- 
fying power  of  the  microscope  estimated  ?  Describe  the  compound  micro- 
scope, and  mention  its  uses. 


SOLAR    MICROSCOPE. 


379 


ject  is  placed  a  little  beyond  the  focus  of  the  object-glass,  by 
which  an  inverted  image  is  formed  near  the  focus  of  the  eye-glass, 
which  farther  magnifies  this  image. 

Fig.  334.  As  the  microscope  is  essentially  composed 

of  two  glasses,  its  magnifying  power  is  the 
product  of  the  magnifying  power  of  each 
of  the  glasses.  Thus,  if  the  object-glass 
magnify  10  times,  and  the  eye-glass  20, 
then  the  diameter  of  the  object  will  be  in- 
creased 200  times,  and  its  surface  40,000 
times.  It  is  evident  that  light  will  be  de- 
composed by  such  instruments,  and  they 
therefore  should  be  made  achromatic. 

The  annexed  diagram,  Fig.  334,  rep- 
resents the  compound  microscope.  The 
glasses  are  placed  in  the  tube,  as  A  B,  I 
K,  m  n  ;  the  mirror,  V,  is  attached  to  il- 

^  luminate  the  object,  and  sometimes  a  eon- 

[_!/     <-JL_Ji  — s]  vex  lens  to  concentrate  the  light  upon  it. 


4.  Solaf  Microscope. — This  beautiful  instrument  consists  of 
two  parts,  one  for  illuminating  the  object,  and  the  other  for  mag- 
nifying it. 

It  consists  of  a  mirror,  M,  Fig.  335,  placed  on  the  outside  of 

Fig.  235. 


a  window,  so  as  to  reflect  the  sun's  rays  into  a  tube,  T,  in  the 
end  of  which  there  is  fixed  a  large  convex  lens,  R,  which  partial- 
ly converges  the  rays.  At  the  other  end  of  the  tube  is  another 
convex  lens,  U  S,  by  which  the  rays  are  brought  to  a  focus.  A 
large  quantity  of  light  being  thus  concentrated,  the  object  to  be 
magnified  is  placed  near  this  focus,  and  beyond  it  there  is  placed 
the  object-glass,  which  magnifies  the  object,  and  throws  its  im- 
age upon  a  white  wall  or  canvas  in  a  darkened  room. 

Describe  the  solar  microscope.     Why  does  it  give  enlarged  images  of 
objects  ? 


380  NATURAL    PHILOSOPHY. 

The  magnifying  power  will  depend  upon  the  focal  distance  of 
the  lens,  as  in  the  simple  microscope.  The  farther  the  screen  is 
removed,  the  larger  the  image  becomes. 

The  oxyhydrogen  blowpipe — Drummond  Light — is  sometimes 
use'd  for  all  these  instruments,  instead  of  the  light  of  the  sun. 

5.  Magic  Lantern. — This  is  similar  to  the  solar  microscope, 
but  more  simple.  It  consists  of  a  metallic  lamp,  A,  Fig.  336, 

Fig.  336. 


a  reflector,  p  q,  and  two  lenses  ;  the  one,  m,  to  illuminate  the  ob- 
ject, and  the  other,  n,  to  magnify  it.  By  this  arrangement  an 
inverted  image  of  the  object  is  thrown  upon  a  screen.  This  is 
used  to  give  a  magnified  representation  of  objects  painted  on  glass. 

6.  Telescopes. — Telescopes  are  similar  in  their  construction  to 
microscopes ;  but  their  glasses  are  so  arranged  as  to  produce  a 
magnified  image  of  distant  objects,  while  the  microscope  is  used 
to  enlarge  those  that  are  near. 

Telescopes  are  of  two  kinds,  refracting  and  reflecting.  Of  the 
refracting  telescopes  there  are  three  principal  varieties — Galileo's, 
the  astronomical,  and  the  terrestrial. 

(1.)  Galileo's  Telescope. — This  consists  of  an  object-glass,  L  N, 
Fig.  337,  and  an  eye-glass,  E  E,  which  is  a  double  concave  lens, 

Fig.  337. 


B 

placed  a  little  nearer  than  the  focus  of  the  object-glass.  If,  then, 
the  lens  L  N  would  bring  the  rays  from  the  object  O  B  to  a 
focus  at  M  I,  this  lens  will  cause  them  to  diverge  so  as  give  an 
erect  image,  i  m.  Opera-glasses  are  constructed  in  this  way,  be- 
cause it  is  desirable  to  have  an  erect  image  of  the  object. 

Describe  the  magic  lantern.     Of  how  many  kinds  are  telescopes? 


REFRACTING    TELESCOPES. 


381 


(2.)  The  Astronomical  Telescope. — In  this  telescope  the  eye- 
glass is  a  double  convex  lens,  of  small  focal  distance,  as  o,  Fig. 
338,  for  the  purpose  of  viewing  the  image  at  c,  which  is  made 

Fig.  338. 

A 

E 


by  the  object-glass,  L.  It  is  similar  to  the  compound  microscope. 
The  image  is  inverted,  and  the  power  of  the  glass  is  found  by  di- 
viding the  focal  distance  of  the  object-glass  by  that  of  the  eye- 
glass. 

(3.)  The  Terrestrial  Telescope. — This  is  like  the  preceding, 
with  two  additional  glasses,  for  the  purpose  of  inverting  the 
image  so  that  objects  may  appear  in  an  erect  position.  Fig-  339 

Fig.  339. 


represents  the  arrangement  in  the  land  telescope  or  spy-glass. 

It  will  be  seen  that  the  two  additional  glasses,  E  E,  F  F, 
have  the  effect  to  invert  the  image  formed  by  the  object-glass, 
L  N.  These  glasses  are  usually  put  into  a  little  tube  which  is 
made  to  slide  into  that  containing  the  object-glass,  and  the 
glasses  are  thereby  adjusted  to  the  object. 

It  has  been  noticed,  page  356,  that  convex  lenses  do  not  con- 
verge all  the  rays  of  a  pencil  which  passes  through  them  to  the 
same  focal  point,  and  hence  there  is  produced  an  indistinctness 
in  the  image  formed.  The  greater  the  thickness  and  diameter  of 
the  lens,  the  greater  the  spherical  aberration. 

The  greatest  aberration  in  a  plano-convex  lens  is  4^-  times  its 
thickness.  If,  however,  the  light  fall  upon  the  convex  surface, 
the  least  aberration  is  lTy¥th  of  its  thickness. 

The  aherration  in  a  double  convex  lens  of  equal  curvatures  is 
of  its  thickness.  If  the  convexities  have  radii  which 


Describe  the  astronomical  telescope.  How  does  the  terrestrial  tele- 
scope differ  from  the  astronomical  ?  What  is  the  greatest  aud  least  spheric- 
al aberration  in  a  plano-convex  lens  ?  What  in  a  double  convex  lens  ? 


382  NATURAL    PHILOSOPHY. 

are  to  each  other  as  1  to  6,  and  parallel  rays  of  light  fall  upon 
the  face  whose  radius  is  1,  the  aberration  is  only  lT£^th  of  its 
thickness,  and  this  is  the  least  to  which  the  aberration  can  be 
reduced  by  a  single  glass,  the  case  being  excepted  where  the 
convex  surface  is  ellipsoidal,  a  form  somewhat  difficult  to  give  to 
lenses. 

As  the  lens  is  thinner,  the  aberration  will  be  less  ;  and  hence 
the  object-glasses  of  large  telescopes  are  thin  lenses  with  long 
focal  distances.  In  some  cases  they  are  composed  of  two  glasses, 
so  that  the  aberrations  may  counteract  each  other.  In  the  eye- 
glasses, in  consequence  of  their  greater  curvature,  it  is  more  dif- 
ficult to  obviate  their  spherical  aberration.  By  using  very  dense 
glass,  or  precious  stones  whose  refracting  index  is  very  high,  as 
the  diamond,  they  may  be  made  much  flatter,  and  in  this  was 
the  difficulty  is  in  a  great  measure  remedied.  Opticians  often 
correct  this  defect  by  grinding  the  surfaces  and  subjecting  them 
to  repeated  trials,  until,  by  actual  experiment,  the  lenses  are  found 
to  give  distinct  images.  They  also  sometimes  take  a  correct 
lens  and  make  a  mold  of  it,  in  order  to  obtain  the  same  curva- 
tures. 

(4:.)  Reflecting  Telescopes. — In  reflecting  telescopes  the  image 
of  a  distant  object  is  formed  by  means  of  a  concave  mirror,  arid 
viewed  by  a  convex  lens.  The  forms  vary  slightly,  and  have 
been  named  after  their  inventors.  Newton's  is  represented  in 
Fig.  340.  A  B  is  a  concave  mirror,  placed  in  one  end  of  a 

Fig.  340. 

A. T,!  O 


tube ;  M  C  is  a  mirror  placed  at  an  angle  of  45°,  to  reflect  the 
rays  which  are  converging  to  the  focus,  m  i,  so  as  to  form  an 
image,  M  I,  on  the  side  of  the  tube,  in  which,  at  L,  a  double 
convex  lens  is  placed,  which  magnifies  the  image. 
(5.)  The  Gregorian  Telescope  has  also  two  mirrors,  a  small 

How  may  the  spherical  aberration  of  lenses  be  remedied  ?     Describe 
the  Gregorian  telescope. 


REFLECTING    TELESCOP 


one  at  C  K,  Fig.  3<y,  which  throws  the 
larger  mirror,  A  R,  through  an  aperture 

Fig.  341. 


where  it  is  observed  by  a  microscope  at  P.  This  is  the  most 
convenient  form  of  reflecting  telescopes. 

(6.)  Herschel's  Telescope  is  similar  to  Newton's,  only,  instead 
of  the  small  mirror  to  reflect  the  image,  it  is  formed  in  the  side 
of  the  tube,  and  observed  by  a  microscope  by  looking  into  its 
open  extremity. 

7.   Size  of  telescopes  and  their  comparative  merits. 

Until  recently  the  reflector  of  Sir  William  Herschel  was  the 
largest  and  most  valuable  instrument  for  astronomical  observa- 
tions in  the  world.  The  speculum  or  reflector  was  4  feet  in  di- 
ameter, and  had  a  focal  length  of  40  feet. 

But  Lord  Rosse,  an  Irish  nobleman,  has  lately  constructed  a 
reflector  6  feet  in  diameter,  with  a  53  feet  focus.  Many  objects 
in  the  heavens,  hitherto  considered  nebulous,  have  been  resolved 
into  clusters  of  stars  by  this  instrument ;  but,  notwithstanding  the 
advantage  derived  from  the  great  amount  of  light  which  it  con- 
centrates upon  the  images  formed,  its  speculum  is  liable  to  be- 
come tarnished  by  exposure,  and  thus  to  furnish  less  distinct  im- 
ages than  refracting  telescopes  of  much  less  size. 

The  refracting  telescope  of  Pulkova,  at  St.  Petersburg,  has 
an  aperture  of  15  inches,  and  a  focal  length  of  22  feet. 

The  refractor  at  Harvard  University  is  of  the  same  dimen- 
sions. These  are  the  largest  refractors  hitherto  constructed. 

The  Cincinnati  refractor  is  somewhat  smaller,  having  an 
aperture  of  12  inches  and  a  focal  length  of  17  feet. 

There  are  several  other  large  refractors  in  the  United  States 
and  in  Europe.  Preference  is  now  given  to  refractors,  since 
large  object-glasses  can  be  made  achromatic.  The  greatest  dif- 

Describe  Newton's  and  HerschePs  telescopes.  Mention  the  size  of  some 
of  the  largest  telescopes.  Which  are  the  best  for  observations,  reflectors 
or  refractors  ? 


384  NATURAL    PHILOSOPHY 

ficulty  is  in  obtaining  flint  glass  sufficiency  dense  and  clear  for 
the  purpose  of  constructing  them.  These  larger  instruments  are 
constructed  at  Munich,  Germany. 

SECTION  V.— THEORIES  OF  THE  NATURE  OF  LIGHT,  WITH  THEIR  ILLUS- 
TRATION AND  APPLICATION. 

THE  two  principal  theories  which  have  been  proposed  to  ex- 
plain the  phenomena  of  light  are  the  emission  or  corpuscular 
theory,  and  the  undulatory  theory. 

I.  Theory  of  Emission. — The  theory  of  emission  supposes  that 
light  consists  of  a  peculiar  luminous  substance,  which  is  emitted 
from  luminous  bodies,  as  the  sun,  and  passes  in  all  directions 
through  space. 

1 .  On  this  theory  the  reflection  of  light  is  the  same  as  that  of 
an  elastic  solid,  falling  upon  surfaces  and  rebounding  from  them, 
and  follows  the  same  laws. 

2.  The  refraction  of  light  is  explained  by  supposing  that  all 
transparent  bodies  have  pores  through  which  the  luminous  par- 
ticles may  pass,  and  that  the  atoms  of  the  body  exert  an  attract- 
ive force  upon  the  luminous  particles,  which,  in  connection  with 
their  velocity,  causes  a  deviation  when  light  passes  from  one  medi- 
um to  another.     The  momentum  of  the  red  ray  is  supposed  to  be 
greater  than  the  violet,  and  hence  it  deviates  less. 

II.  Theory  of  Undulations. — This  theory  assumes  that  light 
is  the  result  of  vibrations,  which  are  propagated  in  an  imponder- 
able substance  called  the  ether,  very  similar  to  the  production  of 
sound  by  vibrations  of  the  air.  The  undulations  of  the  ether  are 
intimately  connected  with,  if  not  caused  by,  vibrations  of  the 
atoms  of  ponderable  matter. 

This  ether  fills  all  space,  and  the  interstices  of  the  most  dense 
bodies.  When  it  is  at  rest,  or  comparatively  so,  there  is  dark- 
ness ;  and  when  in  motion,  within  certain  limits,  waves  of  light 
from  every  point  of  disturbance  proceed  in  all  directions  through- 
out the  regions  of  space. 

What  two  theories  have  been  proposed  to  explain  the  phenomena  of 
light  ?  Describe  the  emission  theory.  How  are  reflection  and  refraction 
accounted  for  on  this  theory  ?  What  does  the  theory  of  undulations  assume  ? 


ETHEREAL    WAVES.  385 

This  theory,  the  elements  of  which  we  now  proceed  to  prove 
and  illustrate,  was  originated  by  Huygens,  but  has  been  recently 
revised  by  several  philosophers,  and,  finally,  perfected  by  Young 
and  Fresnel.  It  offers  the  best  explanation  of  those  phenomena 
of  light  which  we  have  already  described,  and  the  only  consistent 
view  of  those  which  remain  to  be  considered,  such  as  the  inter- 
ference of  light,  polarization,  double  refraction,  dispersion,  and 
diffraction. 

1.  Ethereal  Waves. — Luminous  bodies  vibrate  in  the  same 
manner  as  sonorous  bodies,  but  the  undulations  are  transmitted 
in  the  latter  by  ponderable  matter,  and  in  the  former  by  an  im- 
ponderable ether.  The  ethereal  particles,  like  those  of  water, 
move  in  a  direction  transverse  to  the  direction  of  the  wave ;  but, 
unlike  water  particles,  their  vibrations  are  in  every  plane  that 
can  be  passed  through  the  line  of  the  wave. 

-FV-342.  To  illustrate  the  nature 

I"  c"  d"         of  the  waves  of  light,  let  A 

.ooOQr°0o,       ?  B,  Fig.  342,  be  a  row  of 

5      ethereal  particles  at  rest. 
c  ~cL  When  they  are  set  in  mo- 

tion, they  will  move  in  the  direction  represented  by  a  a',  b  b',  &c., 
at  right  angles  to  A  B.  If  the  molecule  a'  be  moved  to  a",  and 
thence  back  to  a1,  it  will  attain  a  velocity  which  will  carry  it  to  a, 
and,  like  a  stretched  cord,  having  attained  its  greatest  distance 
from  the  line  of  rest,  will  return  again  to  a'.  The  line  a  a"  is  the 
amplitude  of  its  vibrations.  Now  if  all  the  ethereal  molecules  be- 
tween A  and  B,  as  b',  c',  d',  begin  to  move  in  succession  and  in 
the  same  manner  as  a',  only  a  little  later,  there  will  be  produced 
a  wave,  which  is  represented  by  the  curve  line  A  a"  b  c"  d  B. 

When  a'  has  completed  one  vibration  and  commences  upon  the 
second,  the  particle  c'  will  begin  to  move  for  the  first  time  ;  and 
this,  as  we  have  seen,  determines  the  length  of  a  wave  ;  that  is, 
the  distance  between  two  particles  of  ether  in  the  same  state  of 
vibration  is  the  length  of  a  wave  of  light. 

The  length  of  the  wave  in  the  different  colors  is  not  the  same, 
as  we  shall  presently  show,  it  being  longest  in  red,  and  shortest 
in  violet  light. 

How  do  luminous  bodies  vibrate  1  How  do  waves  of  light  differ  from 
those  of  water  and  air  ?  Illustrate  by  diagram  the  nature  of  ethereal  waves. 

R 


386  NATURAL    PHILOSOPHY. 

The  ethereal  molecules  at  b  b',  or  at  half  a  wave  length,  will 
be  in  opposite  states  of  vibration ;  and  hence  all  those  particles 
which  are  removed  £,  f ,  f ,  or  1  of  a  wave  length  from  each  other 
on  the  line  of  the  ray  are  affected  by  equal  and  opposite  veloci- 
ties, while  those  molecules  which  are  once,  twice,  or  any  number 
of  times  a  wave  length  from  each  other,  move  in  the  same  direc- 
tion, and  with  equal  velocities. 

It  will  be  seen  that,  like  air  and  water  waves,  the  ethereal 
undulations  move  in  direct  lines,  and  in  all  directions,  from  the 
point  of  disturbance  ;  but,  as  has  been  observed,  they  differ  from 
both  in  the  circumstance  that,  excepting  in  certain  cases,  the 
particles  may  vibrate  in  every  plane  transverse  to  the  direction 
of  the  wave. 

III.  Interference  of  Light. — We  have  shown  (p.  217,  218) 
how  two  water-waves  or  two  air-waves  may  interfere  and  in- 
crease, or  destroy  each  other's  effects.  It  remains  now  to  notice 
the  same  fact  in  reference  to  two  rays  or  waves  of  light. 

Thus,  let  the  two  rays  of  ^  Fig.  343. 

light,  A  B,  C  D,  Fig.  343, 
cross  each  other  at  a  very  C 
acute  angle  at  e. 

1.  If  the  distance  trav- 
ersed by  the  ray  A  B,  be- 

fore  reaching  the  point  e,  be  equal  to,  or  once,  twice,  or  any  mul- 
tiple of  a  wave  length  greater  than  that  traversed  by  the  ray  C 
D,  then  the  particles  of  ether  transmitting  the  wave  at  e  will  be 
moving  in  the  same  direction,  and  with  equal  velocities ;  and 
hence  their  effect  will  be  doubled.  As  the  amplitude  of  the  vi- 
brating particles  at  that  point  will  be  doubled,  the  light  will  be 
twice  as  intense. 

2.  But  if  one  of  the  rays  has  preceded  the  other  by  half  the 
length  of  a  wave,  as  E  F,  G  H,  or  an  odd  multiple  of  half  a 
wave  length,  that  is,  £,  f ,  f ,  &c.,  of  a  wave  length,  then  at  the 
point  i,  where  they  cross  each  other,  the  molecules  of  ether  will 

What  is  meant  by  interference  of  light  ?  Illustrate  by  diagram  the  con- 
ditions of  interference.  Under  what  conditions  will  two  rays  destroy,  in- 
crease, or  diminish  each  other's  effects  ? 


LENGTH    OF    LUMINOUS    WAVES.  387 

be  acted  upon  by  equal  and  opposite  forces,  interference  will  take 
place,  and  total  darkness  will  be  produced. 

3 .  But  if  the  difference  in  the  distance  of  two  rays  from  their 
source  is  a  little  less  or  greater  than  a  whole  wave  length,  then 
there  will  be  an  increase  of  light  where  the  two  rays  cross,  bat 
its  intensity  will  not  be  twice  as  great ;  or, 

4.  If  the  difference  is  a  little  less  or  greater  than  half  a  wave 
length,  or  some  odd  multiple  of  half  a  wave  length,  then  there 
will  be  a  diminution  of  light  where  the  two  rays  cross,  but  the 
light  will  not  be  entirely  destroyed,  and  the  intensity  will  be  in- 
creased or  diminished  as  these  limits  are  more  nearly  approached. 

5.  The  intensity  of  light  depends  upon  the  amplitude  of  the 
vibrating  particles  ;  but  its  color  depends  upon  their  frequency  of 
vibration.     In  this  respect  there  is  an  exact  analogy  between 
light  and  sound.     A  bright  light,  like  a  loud  tone,  depends  upon 
the  amplitude  of  the  waves  ;  and  different  colors,  like  high  tones, 
depend  upon  the  rapidity  of  the  undulations.* 

Application  of  the  Laws  of  Interference. — The  laws  of  inter- 
ference enable  us  to  explain  many  phenomena  which  are  wholly 
irreconcilable  with  the  emission  hypothesis. 

1.  Length  of  Luminous  Waves. — If  a  ray  of  red  light  from 
a  luminous  point  fall  upon  a  screen  of  white  paper,  and  then  an- 
other ray  from  another  point  be  thrown  upon  the  same  spot,  the 
effect  will  vary  according  to  the  relative  distances  of  the  two 
points  from  the  screen. 

If  the  difference  of  the  distances  of  the  two  points  from  the 
screen  be  the  0  -0000256th  of  an  inch,  or  any  multiple  of  this  dis- 
tance, the  second  ray  will  double  the  effect ;  but  if  the  difference 
in  the  length  of  the  rays  from  their  source  is  £,  f ,  f ,  &c.,  of  the 
0-000025 6th  of  an  inch,  then  the  second  ray  will  produce  entire 
darkness ;  and  if  #ie  difference  is  l£th,  2£th,  &c.,  of  this  same 
quantity,  the  intensity  of  the  light  will  not  be  increased  by  the 
second  ray. 

*  Professor  Snell,  of  Amherst  College,  has  invented  an  apparatus  by 
which  the  vibrations  of  the  ethereal  molecules  are  mechanically  represent- 
ed, and  the  nature  of  the  wave  experimentally  illustrated. 

Upon  what  does  the  intensity  of  light  depend  ?  Upon  what  does  the 
color  depend  ?  How  is  the  length  of  a  wave  determined  ? 


388  NATURAL    PHILOSOPHY. 

If  violet  rays  are  employed  the  same  effects  will  be  produced, 
if  the  difference  of  the  paths  from  the  two  points  is  O'OOOO  174th 
of  an  inch. 

The  other  colored  rays  will  exhibit  the  same  phenomena,  but 
the  distances  must  be  intermediate  between  these  two  quantities. 
Two  rays  of  white  light  will  also  increase  or  diminish  the  brill- 
iancy of  the  spot  on  the  screen,  or  produce  total  darkness. 

These  phenomena  are  evidently  due  to  interference ;  and  as 
two  waves  interfere  and  double  the  intensity  of  the  light  only 
when  the  distance  from  their  source  to  the  screen  is  a  whole  wave 
length,  or  some  multiple  of  a  wave  length,  and  destroy  each  oth- 
er's effects  only  when  their  distance  differs  by  half  a  wave  length, 
or  some  odd  multiple  of  half  a  wave  length,  we  are  enabled  by 
these  experiments  to  determine  the  lengths  of  the  waves  of  red, 
violet,  and  all  the  other  colored  rays. 

The  following  table  gives  these  lengths,  an  inch  being  divided 
into  ten  million  parts. 

Red    light 256  ten  miflionths  of  an  inch. 


Orange 

Yellow 

Greeft 

Blue 

Indigo 

Violet 


240 
227 
211 

196 
185 
174 


2.  Number  of  Vibrations  per  Second. — Now  it  is  a  law  of 
undulations  that  their  number  will  be  inversely  as  the  length  of 
the  waves  ;  that  is,  if  the  least  refrangible  red  waves  were  just 
twice  the  length  of  the  most  refrangible  violet  waves,  they  would 
vibrate  only  half  as  fast,  as  there  would  be  two  vibrations  of  the 
violet  waves  for  one  of  the  red,  which  recent  investigations,  it  is 
said,  prove  to  be  the  fact.  We  have,  therefore,  only  to  divide 
the  distance  which  a  ray  of  light  travels  in  a  second,  195,000 
miles,  by  the  length  of  the  waves  of  each  color,  to  determine  the 
number  of  vibrations  per  second.  This  estimate  will  give  the 
number  for  the  red  waves  about  482  millions  of  millions ;  for 

How  is  the  number  of  vibrations  in  luminous  waves  determined  ?  Men- 
tion the  mode  of  determining  the  length  of  the  waves  of  light. 


NEWTON'S    RINGS.  389 

violet,  710  millions  of  millions  ;  for  orange,  502  millions  of  mill- 
ions ;  and  for  blue,  628  millions  of  millions  of  times  per  second  ! 
But  is  it  possible  to  measure  so  small  spaces  as  the  174  ten 
millionth  of  an  inch  ?  For  this  important  discovery  we  are  in- 
debted to  the  genius  of  Newton.  It  was  accomplished  by  means 
of  the  following  experiments  : 

Upon  a  plane  piece  of  glass  there  was 
piaced  a,  segment  of  a  sphere  of  great  focal 
length,  Fig.  344,  and  the  two  firmly  secured 
together  by  clamps,  so  that  the  segment 
would  touch  the  plane  in  a  single  point.  On 
looking  through  this  lens  toward  an  open 
window,  there  was  seen  at  the  point  of  contact  a  dark  spot,  sur- 
rounded by  seven  rings  of  vivid  colors,  which  are  called  Neiuton's 
Rings. 

The  colors  from  the  dark  spot  succeed  each  other  in  the  follow- 
ing order  :  black,  very  faint  blue,  white,  yellow,  orange,  and  red. 
These  colors  are  evidently  produced  by  the  interference  of  the 
rays  reflected  or  transmitted  from  the  two  surfaces,  which  are 
nearly  in  contact,  viz.,  the  lower  surface  of  the  spherical  segment 
and  the  surface  of  the  plane,  between  which  there  is  a  stratum 
of  air ;  that  is,  the  light  coming  from  the  curved  surface  of  the 
lens  and  that  from  the  plane  meet  the  eye  from  different  dis- 
tances, by  which  some  of  the  colored  waves  interfere,  and,  being 
taken  from  white  light,  colors  are  necessarily  produced. 

If  the  light  used  in  this  experiment  is  homogeneous,  as  red  or 
violet,  then  the  rings  will  be  of  the  same  color,  with  concentric 
circles  of  black. 

The  size  of  the  riags  and  the  spaces  were  found  to  vary  with 
the  color  employed,  being  largest  in  red  and  smallest  in  violet. 

Newton  was  enabled  to  measure  these  rings  and  the  spaces  be- 
tween them,  and  he  found  that  the  squares  of  the  diameters  of 
the  brighest  portions  «of  each  ring  were  as  the  odd  numbers  1,  3, 
5,  7,  &c.,  and  that  the  squares  of  the  diameters  of  the  darkest 
parts  were  as  the  even  numbers  0,  2,  4.  6,  &c.  ;  and,  consequent- 
Describe  the  experimaaats  of  Newton,  and  the  laws  which  he  diseov- 
ered. 


390 


NATURAL    PHILOSOPHY. 


ly,  that  the  intervals  between  the  two  glasses  at  these  points 
must  be  in  the  same  ratio ;  and,  knowing  the  curvature  of  the 
lens  and  the  breadth  of  the  rings,  he  found  that  the  thickness  of 
the  air  between  the  glasses,  at  the  darkest  part  of  the  first  ring, 

was  g-j  £o  otn  °f  an  inch-  fte- 345- 

To  illustrate  how  this  was  done,  let 
P  P',  Fig.  345,  be  a  plane  of  polished 
glass,  A  F  B  C  the  section  of  a  lens 
lying  upon  it,  and  let  E  C  be  the  di- 
ameter of  a  sphere,  of  which  the  lens 
is  a  segment.  Suppose  C  D  to  be  the 
breadth  of  this  dark  ring,  B  D  will  be 
the  thickness  of  the  air  at  the  point  D. 
This  is  equal  to  C  F,  which  is  a  known 
quantity  ;  and  from  this  measurement 
he  deduced  the  thickness  of  the  air  corresponding  to  each  color  in 
the  several  rings ;  and  hence  the  lengths  of  the  waves  were  di- 
rectly determined,  as  in  the  preceding  table.  The  light  in  these 
experiments  must  fall  perpendicularly  upon  the  lens.  If  the  rays 
are  at  an  oblique  angle,  the  rings  will  vary  in  width. 

3.  Color  of  Bodies. — It  follows  from  the  above  experiments 
that  the  colors  of  bodies  are  in  many  cases  due  to  the  thickness 
of  their  laminsB ;  that  is,  the  rays  transmitted  or  reflected  from 
the  upper  and  under  surfaces  of  the  laminsB  interfere  with  each 
other,  and  color  is  the  result.  If,  for  example,  the  thickness  of 
the  film  be  equal  to  the  length  of  the  wave  of  red  light,  or  to  any 
multiple  of  it,  then,  by  interference,  the  red  light  will  be  doubled. 
It  is  on  this  principle  that  a  soap  bubble,  as  it  is  enlarged,  and 
the  thickness  of  the  film  diminished,  presents  us  with  the  several 
colors  of  the  spectrum. 

The  iridescence  observed  in  some  mineral  substances,  as  mica, 
anthracite  coal,  &c.,  is  due  to  thin  laminaB,  or  to  thin  strata  of 
air.  The  feathers  of  small  birds  often  present  the  most  beau- 
tiful and  variegated  appearance ;  hence  the  thickness  of  a  sub- 
stance may  be  determined  by  the  kind  of  light  which  it  reflects 
or  transmits.  The  colors  of  bodies  were  explained  by  the  absorp- 
tion of  some  rays  and  the  reflection  of  others  (p.  362)  ;  but  ab- 


Illustrate  the  mode  of  measuring  the  length  of  waves  of  light.    How  are 
the  colors  of  bodies  explained,  and  upon  what  do  they  depend  ? 


THEORY    OF    UNDULATIONS. 


391 


sorption  itself  is  due  to  interference  produced  by  internal  reflec-. 
tions. 

It  has  been  supposed  to  be  more  difficult  to  reconcile  the  phe- 
nomena of  absorption  with  the  wave  theory  than  with  the  emis- 
sion theory ;  but  it  is  difficult  to  understand  how  a  surface  can 
destroy  luminous  particles  ;  it  is  at  least  conceivable  that  it  may 
destroy  the  motion  of  ethereal  molecules,  by  giving  to  them  so  many 
internal  reflections  that  they  shall  counteract  each  other's  effects. 
4.  The  dispersion  of  light,  or  its  ref Tangibility,  is  also  ex- 
plained by  the  law  of  interference. 

Thus,  if  we  allow  a  ray  of  light  to  pass  through  a  pin-hole 
Fig.  346.     upon  a  white  screen,  there  will  be  produced  circles 
of  colored  light,  which  will  vary  with  the  distance  of 
the  screen  from  the  aperture  ;  or,x 

If  a  fine  slit  be  made  in  a  card,  and  it  be  held  near 
the  eye,  and  directed  to  the  solar  image,   or  to  a 
light  of  any  kind,  as  a  candle,  there  will  be  seen  a 
series  of  colored  bands,  with  a  white  stripe  in  the  cen- 
ter, as  in  Fig.  346.    The  brilliancy  of  the  colors  fades 
on  each  side  of  the  center,  until,  at  the  seventh  stripe, 
they  become  invisible.     When  homogeneous  light  is  thus  viewed, 
Fig.  347.  there  will  be  seen  alternate  colored  and  black 

stripes,  as  in  Fig.  347. 

These  phenomena  are  explained  by  the  fact 
that  the  rays  which  pass  directly  through  the 
aperture,  at  right  angles  to  it,  strengthen  each 
other,  and  produce  a  bright  stripe  in  the  mid- 
dle similar  to  the  color  used ;  but  the  sides  of 
the  aperture  give  rise  to  new  waves  which 
interfere  with  each  other,1*  on  each  side,  and 
destroy  each  other's  effects  ;  and  hence,  if 
one  color  is  used,  black  stripes  will  be  formed. 
Still  further  from  the  center  the  rays  will 

*  This  fact  was  shown  in  reference  to  water-waves  on  page  219,  called 
inflection  of  waves. 


How  is  the  dispersion  of  light  explained?     Mention  the  experiments 
from  which  to  illustrate  and  prove  this  view  of  dispersion. 


392 


NATURAL    PHILOSOPHY. 


again  coincide,  and  we  shall  have  a  bright  stripe,  and  then,  still 
further,  a  black  stripe,  &c. 

When  white  light  is  used  there  will  be  a  white  stripe  in  the 
center,  and  colored  stripes  on  each  side,  for  the  same  reason  as 
given  above. 

This  general  result  may  be  produced  in  a  great  variety  of 
ways.  By  passing  light  through  fine  wire  gauze,  or  the  feathers 
of  small  birds,  we  may  observe  a  most  beautiful  play  of  colors. 

5.  It  is  due  to  the  same  laws  of  interference  that  there  arises 
what  is  called  the 

Diffraction  of  Light.  —  If  a  small 
beam  of  light  be  admitted  into  a  dark- 
ened room,  and  a  knife-blade  held  in  it, 
there  will  be  produced  a  series  of  color- 
ed fringes,  or,  rather,  dark  and  colored 
fringes.  The  ray  appears  to  bend  around 
the  blade,  and,  by  interference,  produces 
the  appearance  represented  in  Fig.  348, 
where  K  N  represents  the  blade,  F  K.  N 
the  ray,  and  S  S  the  screen.  This  is  the 
reason  that  the  shadows  of  small  objects, 
as  a  hair,  are  fringed.  The  same  will 
take  place  whenever  rays  of  light  pass  by  TV  HJ 

a  thin  edge,  or  through  an  aperture.     These  phenomena  are  in- 
capable of  any  consistent  explanation  by  the  corpuscular  theory. 

IV.  Polarization  of  Light. — If  a  ray  of  light  is  reflected  or 
transmitted  at  certain  angles  of  incidence,  it  is  rendered  incapa- 
ble of  being  again  reflected  or  transmitted,  excepting  at  certain 
angles  of  incidence. 

In  such  cases  the  ray  is  said  to  be  polarized.  This  property 
may  be  impressed  upon  light  in  several  ways. 

\.  Polarization  by  Reflection. — If  we  take  a  polished  glass 
plate,  A  B,  Fig.  349,  and  allow  a  ray  of  light  to  fall  upon  it,  as 
a  6,  at  an  angle  of  35°  25',  most  of  it  will  be  reflected  in  the  di- 

What  is  diffraction,  and  how  is  it  explained  ?  When  is  a  ray  of  light 
said  to  be  polarised  ?  Describe  the  mode  of  polarizing  a  ray  of  light  by 
reflection. 


POLARIZATION    OF    LIGHT.  393 

*• 349-  rection  b  c.    If  this  ray 

then  fall  upon  a  second 
plate,  C  D,  placed  par- 
allel to  the  first,  it  will 
be  again  reflected  to  d; 
but  if  the  plate  C  D  be 
revolved  upon  the  line 
b  c  as  an  axis,  the  quan- 
tity of  light  reflected 
will  constantly  diminish 
until  the  plate  is  at  right 
\  angles,  or  90°,  when  the 

reflection  will  almost  entirely  cease.  On  continuing  the  revolu- 
tion, light  will  again  begin  to  be  reflected  from  its  surface  until 
it  has  reached  180°,  when  it  will  reflect  light  as  at  first.  By 
turning  the  plate  another  quarter  of  a  revolution,  or  270°,  the 
power  of  reflection  will  nearly  cease  again,  and  become  restored 
when  it  has  completed  an  entire  revolution. 

The  ray  has,  therefore,  a  peculiar  property  imparted  to  it  by 
one  reflection,  which  renders  it  less  capable  of  reflection  from  a 
second  surface  at  right  angles  to  the  first.  The  whole  of  the  ray 
will  be  reflected  only  when  the  second  plate  is  parallel  with  the 
first,  or  when  it  is  revolved  upon  the  polarized  ray  as  an  axig, 
180°,  so  that  the  polarized  and  reflected  ray  in  each  case  may 
be  in  the  same  plane.  A  plane  passing  through  the  lines  made 
by  the  polarized  and  .reflected  rays,  as  b  c  and  c  d,  is  called  the 
plane  of  polarization.  A  part  of  the  incident  light  will  be  trans- 
mitted unless  the  back  of  the  glass  is  covered  or  painted  black. 

The  angle  at  which  incident  light  must  fall  to  become  polar- 
ized depends  upon  the  substances  used,  or  upon  their  power  of  re- 
fraction. The  incident  ray  must  fall  at  such  an  angle  that  the 
reflected  ray  shall  make  an  angle  of  90°  with  the  refracted  ray, 
on  the  supposition  that  it  were  transmitted  through  the  substance. 
For  experiments  on  the  polarization  of  light  by  reflection,  two 
mirrors  are  so  arranged  in  a  frame  that  they  may  be  placed  at 
any  angle  to  each  otfe.«r  ;  one  of  them  is  fitted  to  revolve,  and  has 
an  index  to  note  the  degrees,  and  thereby  determine  its  position 
in  reference  to  the  other  mirror. 

What  is  the  piano  of  polarization  ?  Upon  what  does  the  angle  of  polar- 
ization depend  ? 

R2 


394 


NATURAL    PHILOSOPHY. 


Fig.  350. 


Thus,  Figure  350  represents  one 
form  of  the  polariscope.  It  consists 
of  a  tube,  A  B,  with  two  mirrors ; 
one  of  black  glass  at  «,  with  a  gradu- 
ated arc,  e,  by  which  it  may  be  placed 
at  any  angle.  It  also  may  be  revolved 
upon  the  axis  of  the  tube,  and  the 
amount  of  rotation  noted  on  the  grad- 
uated circle  b.  At  the  other  end 
there  is  a  second  mirror,  d,  which  is 
arranged  in  a  similar  manner. 

2.  Polarization  by  Refraction. — If  we  cut  from  a  transparent 
tourmalin  two  plates,  parallel  with  Fig,  351. 

the  axis,   about  ^Vtn  °f  an  mc^  m 
thickness,  as  c  d  and  e  f,  Fig.  351, 

and  pass  a  ray  of  light  through  the  

first,  c  d,  the  ray  will  pass  through 
the  second,  provided  that  its  axis  is 
parallel  with  the  first,  as  ef;  but  if  e/be  turned  around  90°, 
into  the  position  represented  by  g  h,  the  ray  will  be  wholly  ob- 
structed. At  180°  it  will  be  transmitted  again,  and  at  270° 
obstructed.  In  this  experiment  the  ray  has  become  polarized  by 
the  first  plate,  so  that  it  will  be  transmitted  by  the  second  plate 
only  at  certain  angles  in  the  plane  of  polarization. 

That  the  property  impressed  upon  the  ray  by  transmission  is 
the  same  as  that  produced  by  reflection,  is  proved  by  the  fact 
that,  if  a  tourmalin  be  used  instead  of  the  second  glass  plate  in 
Fig.  349,  the  ray  will  not  be  transmitted  when  its  axis  is  at  an 
angle  of  90°  with  the  plate. 

Glass  plates  will  polarize  light  by  transmission  ;  but  to  render 
the  effect  complete,  several  glasses  must  be  used.  A  piece  of 
glass,  and  many  other  substances,  may  be  made  to  polarize  light 
by  pressure,  that  is,  by  rendering  one  part  more  dense  than  an- 
other. 

Theory. — The  phenomena  of  polarization  may  be  explained  on 
the  theory  of  undulations,  by  supposing  that  the  vibrations  of  the 
ethereal  molecules  in  radiant  light  take  place  in  every  plane  per- 
pendicular to  the  path  of  the  ray,  and  that  the  effect  of  reflection 
or  refraction  is  to  confine  these  vibrations  to  one  plane,  so  that 

How  is  light  polarized  by  refraction  ?  Illustrate  by  diagram.  How  are 
the  phenomena  of  polarization  explained  ? 


DOUBLE    REFRACTION. 


395 


the  wave  becomes  like  that  of  a  stretched  cord,  or  of  particles  of 
Fig.  352.  water,  or  like  a  strip  of  paper,  which  may  be 

slid  through  between  two  grates  in  one  position 
and  not  in  another. 

Fig.  352  may  represent  the  condition  of  a 
ray  when  it  is  to  be  transmitted  ;  the  strip  will 
pass  through  in  the  position  c  d, 
and  not  in  the  position  ef. 

Fig.  353  may  represent  the 
condition  of  the  wave  when  it 
falls  upon  a  reflecting  surface. 

Thus  the  ray  a,  falling  upon 
the  mirror  A  B,  is  reflected  so 
that  the  particles  of  ether  vibrate 
only  in  the  plane  C  D.  When 
they  fall  upon  a  second  plate 
similarly  situated,  they  will  be 
reflected,  but  in  other  positions  of  the  plate  will  be  but  partially 
reflected,  or  not  reflected  at  all. 

V.  Double  Refraction. — There  are  many  transparent  substan- 
ces which  have  the  property  of  separating  an  incident  ray  of  light 
into  two  emergent  rays.  Iceland  spar  and  several  other  crystals 
possess  this  power  in  an  eminent  degree. 

.  354.  1 .  The  property  of  double  re- 

fraction  may  be  shown  experi- 
mentally by  taking  a  crystal  of 
Iceland  spar,  A  B  C  X,  Fig- 
ure 354,  and  causing  a  ray  of 
light,  as  R  r,  to  be  transmitted 
through  it.  The  ray  will  be 
separated  into  two  rays,  r  E 
and  r  O,  which  will  emerge  as 
E  o,  O  0,  parallel  to  each  other. 
The  degree  of  separation  will 
depend  upon  the  thickness  of  the  crystal.  The  ray  r  O  is  called 
the  ordinary  ray,  because  it  is  refracted  according  to  the  ordi- 
nary law  ;  that  is,  it  remains  in  a  plane  perpendicular  to  the  re- 


What  is  double  refraction,  and  how  may  it  be  exhibited  ? 


396 


NATURAL    PHILOSOPHY. 


fracting  surface  at  the  point  of  incidence,  while  E  o  is  termed 
the  extraordinary  ray. 

By  laying  such  a  crystal  upon  a  line,  or  any  small  object,  and 
looking  through  it,  it  will  appear  double. 

The  crystal,  however,  will  not  separate  the  ray  if  it  transmits 
it  in  certain  directions. 

For  if  a  plane  be  drawn  through  the  diagonal 
edges  of  the  obtuse  angles  of  the  crystal,  Fig. 
355,  rays  of  light  parallel  or  perpendicular  to 
the  line  a  b,  which  joins  the  obtuse  angles,  and 
called  the  optic  axis  of  the  crystal,  will  not  be 


Iceland  spar  has  but  one  optic  axis,  but  there  are  many  crys- 
tals which  have  two,  along  which  a  ray  of  light  will  suffer  only 
ordinary  refraction. 

In  some  crystals  the  extraordinary  ray  is  refracted  toward  the 
optic  axis,  as  those  of  quartz  and  ice,  and  are  called  positive.  In 
others,  the  lay  is  refracted  from  this  axis,  as  those  of  Iceland 
spar,  beryl,  and  tourmalin,  and  are  called  negative  crystals. 

Theory. — The  phenomenon  of  double  refraction  is  explained  by 
supposing  that  the  ethereal  medium  in  the  crystal  is  not  equally 
elastic  in  all  directions.  Its  vibrations  will,  therefore,  be  trans- 
mitted with  unequal  velocities,  and  this  would  cause  a  division 
of  the  ray. 

2.  Polarization  by  Double  Refraction. — When  a  ray  of  light  is 
separated  by  double  refraction,  the  emergent  rays  are  both  polarized. 

This  is  proved  by  looking  at  the  two  images  formed  through  a 
plate  of  tourmalin.  When  it  is  in  one  position,  both  images  may 
be  seen ;  but,  as  the  tourmalin  is  revolved,  one  of  the  images  in- 
creases, while  the  other  diminishes  in  brightness,  and  when  one 
has  attained  its  greatest  brilliancy,  the  other  will  vanish.  In  one 
position  of  the  tourmalin  the  ordinary  ray  is  reflected,  and  the 
extraordinary  transmitted  ;  but  when  it  is  turned  90°,  the  extra- 
ordinary ray  is  reflected,  and  the  ordinary  ray  transmitted.  On 
the  other  hand,  if  a  polarized  ray  be  sent  through  the  crystal,  it 
can  not  be  separated  into  two  emergent  rays. 

How  is  double  refraction  accounted  for  ?  What  is  the  condition  of  the 
double  refracted  rays  ? 


POLARIZED    LIGHT.  397 

3.  Action  of  thin  Lamince  on  Polarized  Light. — When  polar- 
ized light  is  passed  through  thin  laminae  of  crystals,  it  exhibits  some 
of  the  most  beautiful  appearances  in  the  whole  science  of  optics. 

Thus,  between  two  reflecting  glass  plates,  Fig.  356,  place  a 

Fig.  356. 


thin  scale  of  mica  or  gypsum,  D  E,  so  that  a  ray  of  light,  after 
being  polarized  by  the  plate  A,  may  pass  through  it  in  the  direc- 
tion A  C,  upon  the  second  plate,  and  reflected  to  E.  The  eye 
at  this  point  will  perceive  the  most  beautiful  colors  in  certain  po- 
sitions of  the  polarizing  plates. 

If  the  two  plates  are  placed  at  right  angles  to  each  other  be- 
fore the  mica  is  introduced,  the  ray  will  not  be  seen  at  E,  as  has 
been  before  shown ;  but  on  introducing  the  mica,  and  viewing 
the  reflected  ray  at  E  through  a  plate  of  tourmalin,  the  colors 
will  immediately  appear.  The  tints  will  vary  with  the  thick- 
ness of  the  mica. 

If  the  mica  be  revolved  on  the  axis  A  C,  there  will  be  two 
positions  where  the  colors  will  disappear,  and  these  positions  are 
when  the  lines  D  E  or  F  G  are  either  parallel  or  perpendicular 
to  the  polarizing  plane  II  A  C  and  ACE. 

But  if  the  second  glSss  plate  revolve,  and  the  plate  of  mica  re- 
main stationary,  then  there  will  be  presented  in  the  course  of  the 
revolution  complementary  colors  in  the  following  order  : 

If  the  tint  is  red,  after  revolving  the  second  plate  45°  it  will 
vanish,  and  a  pale  green  will  begin  to  be  seen,  until,  at  90°,  it 
attains  its  highest  brilliancy,  but  ceases  when  the  plate  reaches 

Describe  the  effect  of  plates  of  mica  upon  polarized  light.  What  effect 
is  produced  by  revolving  the  mica  plate  ? 


398 


NATURAL    PHILOSOPHY. 


135°.     At  this  point  a  bluish  red  commences,  and  reaches  its 
maximum  at  180°. 

These  are  complementary  colors  ;   that  is,  the  two  tints  at 
their  maximum  brilliancy  will  produce  white  light  when  com- 
.  357.  bined  ;    for,  if  we  view   the 

mica  plate  through  an  achro- 
matic lens,  two  images  will 
appear  at  the  same  time,  and, 
if  thrown  upon  each  other,  as 
in  Fig.  357,  they  will  produce 
white  light. 

If,  instead  of  the  mica,  we 
insert  thin  slices  of  a  crystal  having  one  optical  axis,  and  cut  at 
right  angles  to  it,  we  may  obtain  a  series  of  colored  rings  with 
dark  stripes,  and  a  cross  in  the  middle,  which  will  be  light  or 
dark  according  to  the  position  of  the  polarizing  plates.  Fig.  358 
represents  these  two  appearances. 

Fig.  358. 


If  the  slices  are  cut  from  crystals  having  two  optic  axes,  we 
observe  a  double  system  of  rings,  as  in  Fig.  359,  which  repre- 

F&.259. 


How  may  a  series  of  colored  rings  be  produced  by  polarized  light  ? 


COLORS  OP  THIN  PLATES.  399 

sents  the  two  appearances  in  the  two  positions  of  the  polarizing 
plates. 

The  different  colors  thus  produced  are  due,  as  we  have  before 
shown,  to  interference,  the  colors  varying  according  to  the  posi- 
tion and  thickness  of  the  plates  which  are  introduced. 

Uncrystalline  bodies  will  not  give  similar  results,  unless  they 
are  unequally  heated  or  compressed.  A  piece  of  glass,  by  press- 
ure, may  be  made  to  exhibit  similar  colors  when  placed  in  the 
polari  scope. 

There  is  still  another  class  of  crystals  which  are  capable  of 
polarizing  light  in  a  manner  different  from  any  hitherto  consid- 
ered. The  ray  in  such  cases  becomes  polarized,  so  that  the  ethe- 
real molecules  move  in  circles  and  ellipses  instead  of  right  lines,  as 
in  all  other  cases,  and  is  said  to  be  circularly  and  elliptically  po- 
larized. 

From  this  general  view  of  the  undulatory  theory  of  light,  it 
appears  that  it  explains  the  phenomena  of  reflection,  refraction, 
and  absorption  equally  well  with  the  emission  theory,  while  there 
are  certain  phenomena,  such  as  those  of  interference,  refrangi- 
bility,  diffraction,  double  refraction,  and.  polarization,  which  can 
be  explained  only  on  this  theory.  It  is,  therefore,  entitled  to  the 
character  of  a  true  theory,  and  to  be  accepted  as  well-established 
scientific  truth.  For  a  more  full  account  of  the  theory,  the  stu- 
dent is  referred  to  larger  works,  as  Whewell's  History  of  the  In- 
ductive Sciences,  and  especially  to  the  works  of  Young  and  Fres- 
nel,  by  whom  this  whole  subject  has  been  most  beautifully  devel- 
oped. Many  of  these  discoveries,  in  their  simplicity,  and  in  the 
variety  of  phenomena  they  explain,  may  well  be  placed  beside 
that  of  universal  gravitation  itself. 

What  is  meant  by  elliptical  and  circular  polarization  ? 


460 


NATURAL    PHILOSOPHY. 


SECTION  VI.— CHEMICAL  EFFECTS  OF  LIGHT,  AND  THE  CONNECTION  BE- 
TWEEN  HEAT,  LIGHT,  AND  ELECTRICITY. 

I.  LIGHT  exerts  certain  specific  influences  upon  chemical  sub- 
stances.    Thus,  if  hydrogen  and  chlorine  gases  are  mixed  in  the 
dark,  no  combination  will  take  place,  but  a  ray  of  sunlight  will 
cause  them  to  unite  with  explosive  energy. 

Nitric  acid  is  slowly  decomposed  when  exposed  to  the  light. 
White  chloride  of  silver,  when  exposed  to  the  solar  ray,  becomes 
black.  Many  other  compounds  are  strongly  acted  upon  by  light. 

But  its  most  useful  action  is  upon  the  salts  of  silver,  by  which 
the  images  of  objects  are  permanently  fixed  on  paper  or  metal,  the 
process  of  which  is  called, 

II.  Photography.— -The  most  important  photographic  pictures 
are  those  produced  by  a  method  discovered  by  Daguerre. 

By  this  process  the  images  of  objects  formed  in  the  camera  ob- 
scura  are  permanently  fixed  on  polished  metallic  plates. 

A  copper  plate  is  thinly  covered  with  silver,  and  very  brightly 
polished  ;  the  plate  is  then  exposed  to  the  vapor  of  iodine  until  it 
exhibits  a  golden-yellow  appearance,  produced  by  a  thin  film  of 
iodide  of  silver.  It  is  then  put  into  the  camera  obscura,  and  the 
image  of  any  object  thrown  upon  it.  After  a  minute  or  so,  the 
time  depending  upon  the  intensity  of  the  light,  the  plate  is  re- 
moved, and  placed  over  a  mercury  bath,  which  is  heated  to  150° 
or  more,  and  the  vapor  of  mercury,  becoming  attached  to  the 
plate,  renders  the  image  visible.  The  plate  is  then  washed  in  a 
solution  of  hyposulphite  of  soda,  which  dissolves  the  iodide,  and 
the  farther  action  of  the  light  is  arrested.  We  then  have  a  bright 
metallic  surface  where  the  iodide  has  not  been  acted  on  by  the 
light,  and  where  it  has  a  thin  film  of  mercury.  By  this  means 
images  become  permanently  fixed  to  the  plate,  and  are  called 
Daguerreotypes* 

*  For  directions  in  taking  photographic  pictures,  the  student  is  referred 
to  H.  H.  Snelling's  "  Art  of  Photography" 

What  chemical  substances  does  light  affect?  How  are  photographic 
pictures  produced  ?  Describe  the  Daguerreotype.  How  are  Talbotypes 
produced  ? 


CONNECTION    OF    LIGHT,    HEAT,   AND    ELECTRICITY.     401 

Talbot  has  produced  pictures  upon  paper,  which  is  prepared 
by  a  chemical  process,  and  rendered  sensitive  to  light.  The  pa- 
per is  exposed  in  the  camera,  and  the  images  fixed  with  bromide 
of  potassium.  These  are  called  Talbotypes,  or  Calotypes. 

Many  vegetable  extracts  are  acted  on  by  light,  and  paper  cov- 
ered with  them  may  be  used  for  pictures. 

Light  promotes  the  decomposition  of  organic  compounds  by 
rendering  the  oxygen  of  the  air  more  active  ;  hence  the  reason 
that  many  substances  fade  when  exposed  to  the  light,  and  soon 
decay.  Light  discharges  or  changes  the  color  of  many  substances 
which  are  exposed  to  its  influence.  Light  also  promotes  the 
growth  of  plants,  by  decomposing  the  carbonic  acid  in  the  leaves, 
and  changing  the  color  green.  The  yellow  ray  seems  mostly 
concerned  in  this  latter  change. 

Plants  always  grow  in  the  direction  of  light  when  confined  in 
a  dark  room. 

Finally,  light  is  essential  to  the  healthful  development  of  ani- 
mal life.  It  is  the  source  of  animal  pleasures;  the  medium 
through  which  we  derive  our  most  important  knowledge  ;  a  sym- 
bol of  purity  and  of  the  highest  felicity  ;  the  robe  of  the  celestial 
inhabitants,  and  of  the  Deity  himself. 

III.   Connection  between  light,  heat,  and  electricity. 

The  analogies  between  light,  heat,  and  electricity  lead  to  the 
inference  that  their  phenomena  all  depend  upon  certain  modifica- 
tions of  the  ethereal  medium,  in  connection  with  the  atoms  of 
ponderable  matter. 

1.  Light  and  heat  originate  under  similar  conditions.     They 
frequently  accompany  each  other,  and  observe  the  same  laws  in 
respect  to  the  phenomena  of  transmission,  reflection,  refraction, 
absorption,  polarization,  interference,  &c. 

2.  The  polarization  and  double  refraction  of  heat  first  noticed 
by  Berard,  and  fully  established  by  Forbes  and  Melloni,  have 
lately  been  re-examined  by  Provostage  and  Desains,  and  the  fol- 
lowing results  obtained  : 

(1.)  When  a  beam  of  heat  is  passed  through  Iceland  spar  it 

What  action  has  light  on  organic  compounds?  Mention  the  analogies 
between  light  and  heat. 


402  NATURAL   PHILOSOPHY. 

is  separated  into  two  portions,  which  are  found  to  be  polarized  in 
the  plane  of  the  section  and  in  a  plane  perpendicular  to  it. 

(2.)  The  intensity  of  a  ray  of  light  in  being  separated  is  divided 
between  the  two  images  which  are  formed,  and  the  same  is  true 
of  a  ray  of  heat. 

(3.)  Polarized  light  and  heat  present  the  same  phenomena 
when  reflected  from  glass  or  from  metallic  surfaces. 

3.  The  connection  between  either  of  the  above  and  electricity 
is  not  so  obvious ;  and  yet  there  are  many  facts  which  show  an 
intimate  relation,  if  not  an  identity,  in  the  fundamental  cause. 

The  late  experiments  of  Professor  Pliicker,  of  Bonn,  have  estab- 
lished the  fact  that  crystals  which  have  the  power  of  double  re- 
fraction possess  magnetic  properties.  The  optic  axes  of  positive 
crystals  are  attracted,  and  of  negative  crystals  repelled,  by  the 
poles  of  a  magnet.  In  fact,  many  crystals  are  true  magnets,  and 
double  refraction  may  therefore  be  closely  connected  with  electric 
currents. 

Mr.  Faraday  has  shown  a  very  intimate  relation  of  light  to 
magnetism. 

The  limits  of  this  work  forbid  a  further  discussion  of  the  sub- 
ject, and  the  student,  it  is  hoped,  will  consult  the  various  scien- 
tific journals  for  further  information.  It  has  not  been  possible  to 
give  any  thing  more  than  an  outline  of  the  undulatory  theory,  or 
of  the  various  phenomena  which  it  explains. 


INDEX. 


A. 


Page 


Acoustics . 225 

Aerolites 199 

Aerometer 131 

Air,  buoyancy  of 178 

"    elasticity  of 160 

"    fountain 172 

"    gun 173 

"    motion  of 180 

"    pressure  of 163 

"    pump 159 

'   "    resistance  of. 178 

Animal  electricity 323 

Archimedes's  screw 153 

Atmosphere,  density  of 184 

"           height  of 186 

"            moisture  of 193 

"            temperature  of ...  187 

"            weight  of 183 

Atoms 13 

"       shape  of 27 

Attraction,  capillary 32 

"          chemical 34 

"          cohesive 25 

"          electrical 35 

"          of  gravitation 35 

B. 

Balance 87 

' '  electrometer 277 

Barker's  mill 144 

Barometer 166 

Bodies,  collision  of 76 

"  properties  of 28 

Brittleness 31 

Burning  glasses 357 


C. 


Page 


Caloric 247 

Camera  obscura 377 

Capstan 89 

Center  of  gravity 67 

Chromatic  aberration 363 

Compressibility 30 

Concave  lens .  353 

Convex  lens 352 

Crane 88 

Crystalline  forms 27 

Cupping 162 

Curve,  balistic 72 

Cycloid 102 

D. 

Density 31 

Double  refraction 395 

Ductility 31 


Echo 233 

Elasticity 29 

Electric  battery 276 

Electrical  fountain 281 

"        light 277 

"        machine 264 

"        pistol 283 

"        spider 275 

"        sportsman 276 

"        tellurian...! 272 

Electricity 260 

"          of  the  atmosphere  . .  286 

Electro-chronograph 322 

Electrography 302 

Electro-magnetism 307 


404 


Electrophorus 265 

Electroscopes 262 

Ethereal  waves 385 

Eyes,  compound 372 

"      simple 372 

F. 

Falling  bodies,  laws  of 61 

"      stars 198 

Fire-balls 198 

Fire  engine 174 

Floating  bodies 133 

Fly-wheel 110 

Force,  centripetal -  73 

"      idea  of 15 

"      nature  of 43 

Forces,  composition  of 56 

"       resolution  of 50 

Fountain,  Hiero's 174 

G. 

Galvanism 275 

Gasometer 180 

Gearing Ill 

Gilding 301 

Gravity,  center  of 67 

"        force  of.. 36 

"        specific 129 

Grove's  battery 297 

Gunnery 73 

H. 

Hail 197 

Halos , 369 

Hardness * 31 

Harp,  JEolian  .,-...w 244 

Hearing,  organs  of „ 246 

"        trumpet 235 

History,  natural 17 

Hunter's  screw. ..•.-..* 108 

Hurricanes 191 

Hydraulic  ram-.... 145 

Hydraulics . . . 138 

Hydrostatic  bellows . 124 

"           press 126 


INDEX. 
Page 


I. 


Inclined  plane 96 

Induction 267 

Inertia 40 

K. 
Kaleidoscope 339 

L. 

Law,  idea  of 15 

Lever 82 

Leydenjar 272 

Life  preservers 135 

Light,  diffraction  of 392 

"      dispersion  of 391 

"      intensity  of. 330 

"      interference  of 386 

"      originof 326 

"     reflection  of 335 

"      refraction  of 345 

"      velocity  of 333 

Lightning  rod 288 

M. 

Machine,  weighing 86 

Magic  lantern 380 

Magnetism 304 

Magneto-electric  induction 313 

Matter,  divisibility  of 19 

"       idea  of 14 

"       impenetrability  of. ....     22 

Measures,  standard  of. 106 

Meteorolites 198 

Micrometer  screw 108 

Microscope,  compound 378 

"  simple 377 

,  "  solar 379 

Mirrors,  curved 337 

"        plane . „ 335 

Motion,  absolute 41 

"       apparent 42 

"       naturally  uniform 47 

"       proportioned  to  force. .     49 

"       real 42 

"       relative 41 


INDEX. 


405 


o. 


Page 


Organs  of  hearing 246 

"       of  voice 245 

Oscillation,  center  of 102 

P. 

Pendulum 101 

Photography 400 

Photometry 331 

Physics 15 

Polariscope 394 

Porosity 28 

Prism 350,358 

Pulley 73 

Pump,  chain 153 

"      condensing 163 

"      forcing 170 

"      lifting 170 

"      Vera's  ..  .153 


Rain 196 

Rainbow 365 

Reflection,  total 347 

Refraction  ..  .345 


Simoon 190 

Smee's  battery 238 

Snow 197 

Sound,  conduction  of 228 

"      reflection  of 230 

"      velocity  of 230 

Spherical  aberration 343 

Spiral  tube 277 

Spirit  level 129 

Steam 249 

"      engine 252 

Stethoscope 235 

Strength  of  materials 114 

Syphon 169 


T. 


Page 


Telegraph,  Bain's 322 

"          House's 322 

"          Morse's 321 

Telescopes,  reflecting 382 

"           refracting 381 

Tenacity 32 

Theory  of  undulations 284 

Thermo-electricity 309 

Thunder  house 28!* 

"        storms 287 

Tone,  musical 236 

"      varieties  of 228 

Tornadoes 192 

Twilight 369 

U. 
Undulations 206 

Universal  discharger 281 

V.  • 

Ventilation 200 

Volta-electric  induction 313 

Voltaic  electricity 293 

W. 
Water,  compressibility  of 152 

"       spouts 192 

"       waves 213 

Waves,  of  air 219 

"       of  sound 226 

Wedge 109 

Weights,  standard  of 105 

Wheels,  horizontal 152 

"        middleshot 152 

"        overshot . ....   151 

"        undershot 152 

Whispering  galleries 234 

Winds 188 

"      trade  ..  .189 


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